## Xu, Junxiang

Compute Distance To:
 Author ID: xu.junxiang Published as: Xu, Junxiang; Xu, Jun Xiang; Xu, Jun-Xiang
 Documents Indexed: 160 Publications since 1990 Co-Authors: 38 Co-Authors with 130 Joint Publications 1,109 Co-Co-Authors
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### Co-Authors

 13 single-authored 47 Zhang, Fubao 27 Wang, Jun 24 Zhang, Dongfeng 18 Zhang, Hui 11 You, Jiangong 10 Shi, Yanling 10 Wang, Xiaocai 8 Xu, XinDong 7 Ding, Jian 7 Lu, Xuezhu 6 Cao, Xiaofei 6 Tian, Lixin 4 Zhu, Min 3 Cheng, Rong 3 Guo, Jingni 3 Jiang, Shunjun 3 Kong, Yuedong 3 Qiu, Qingjiu 2 He, Zhenggang 2 Liao, Wei 2 Liu, Xila 1 Bi, Qiaoyan 1 Chen, Xumei 1 Cheng, Chunrui 1 Du, Miao 1 Geng, Jiansheng 1 Kun, Wang 1 Liang, Jianli 1 Liu, Weihua 1 Lu, Dianchen 1 Ma, Hui 1 Ma, Zhichao 1 Min, Zhu 1 Norrlöf, Mikael 1 Wang, Kun 1 Wang, Shaoping 1 Yang, Renzi 1 Yang, Xiaomei 1 Zheng, Qin
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### Serials

 11 Journal of Mathematical Analysis and Applications 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Mathematical Methods in the Applied Sciences 7 Discrete and Continuous Dynamical Systems 5 Journal of Mathematical Physics 5 Journal of Differential Equations 5 Ergodic Theory and Dynamical Systems 5 Acta Applicandae Mathematicae 5 NoDEA. Nonlinear Differential Equations and Applications 5 Discrete and Continuous Dynamical Systems. Series B 4 Proceedings of the American Mathematical Society 4 Journal of Dynamics and Differential Equations 4 Electronic Journal of Differential Equations (EJDE) 4 Electronic Journal of Qualitative Theory of Differential Equations 4 Qualitative Theory of Dynamical Systems 3 Applicable Analysis 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Science in China. Series A 3 Abstract and Applied Analysis 3 Advanced Nonlinear Studies 3 Scientia Sinica. Mathematica 2 International Journal of Systems Science 2 Journal of Sound and Vibration 2 Nonlinearity 2 Mathematische Zeitschrift 2 Topological Methods in Nonlinear Analysis 2 Calculus of Variations and Partial Differential Equations 2 Regular and Chaotic Dynamics 2 Acta Mathematica Sinica. English Series 2 Communications on Pure and Applied Analysis 2 Boundary Value Problems 1 Computers & Mathematics with Applications 1 Mathematical Notes 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 Applied Mathematics and Computation 1 Automatica 1 Mathematische Nachrichten 1 Mathematika 1 Journal of Nanjing University. Natural Sciences 1 Chinese Annals of Mathematics. Series A 1 Journal of Nanjing University. Mathematical Biquarterly 1 Journal of Southeast University. English Edition 1 International Journal of Adaptive Control and Signal Processing 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Applied Mathematics 1 Differential Equations and Dynamical Systems 1 Journal of Applied Mechanics and Technical Physics 1 Far East Journal of Applied Mathematics 1 RAIRO. Operations Research 1 Annales Henri Poincaré 1 Dynamical Systems 1 Central European Journal of Mathematics 1 Analysis in Theory and Applications 1 1 Journal of Industrial and Management Optimization 1 Journal of Shanghai Jiaotong University (Science) 1 Journal of Zhejiang University. Science A 1 Frontiers of Mathematics in China 1 Acta Mathematica Sinica. Chinese Series 1 Science China. Mathematics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
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### Fields

 82 Dynamical systems and ergodic theory (37-XX) 58 Partial differential equations (35-XX) 40 Ordinary differential equations (34-XX) 30 Mechanics of particles and systems (70-XX) 13 Global analysis, analysis on manifolds (58-XX) 9 Operator theory (47-XX) 5 Systems theory; control (93-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 3 Operations research, mathematical programming (90-XX) 2 Real functions (26-XX) 2 Differential geometry (53-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

117 Publications have been cited 1,052 times in 623 Documents Cited by Year
Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth. Zbl 1402.35119
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2012
Invariant tori for nearly integrable Hamiltonian systems with degeneracy. Zbl 0899.34030
Xu, Junxiang; You, Jiangong; Qiu, Qingjiu
1997
Existence and concentration of positive solutions for semilinear Schrödinger-Poisson systems in $${\mathbb{R}^{3}}$$. Zbl 1278.35074
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2013
Persistence of lower-dimensional tori under the first Melnikov’s non-resonance condition. Zbl 1031.37053
Xu, Junxiang; You, Jiangong
2001
Existence and multiplicity of homoclinic orbits for the second order Hamiltonian systems. Zbl 1204.37067
Wang, Jun; Zhang, Fubao; Xu, Junxiang
2010
Homoclinic orbits for a class of Hamiltonian systems with superquadratic or asymptotically quadratic potentials. Zbl 1231.37033
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2011
Normal form of reversible systems and persistence of lower dimensional tori under weaker nonresonance conditions. Zbl 1075.37020
Xu, Junxiang
2004
On the persistence of degenerate lower-dimensional tori in reversible systems. Zbl 1351.37231
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2015
On the reducibility of a class of linear differential equations with quasiperiodic coefficients. Zbl 1043.34036
Xu, Junxiang
1999
Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation. Zbl 1218.34050
Xu, Junxiang; Jiang, Shunjun
2011
Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems. Zbl 1202.37080
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2010
On small perturbation of two-dimensional quasi-periodic systems with hyperbolic-type degenerate equilibrium point. Zbl 1217.34076
Xu, Junxiang
2011
Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann’s non-degeneracy condition. Zbl 1112.37045
Xu, Junxiang; You, Jiangong
2007
On the reducibility of linear differential equations with quasiperiodic coefficients which are degenerate. Zbl 0897.34011
Xu, Junxiang; Zheng, Qin
1998
On the wave-breaking phenomena for the periodic two-component Dullin-Gottwald-Holm system. Zbl 1298.35121
Zhu, Min; Xu, Junxiang
2012
Degenerate lower dimensional tori in reversible systems. Zbl 1260.37029
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2012
Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann’s non-degeneracy condition. Zbl 1175.37065
Wang, Xiaocai; Xu, Junxiang
2009
A KAM theorem of degenerate infinite dimensional Hamiltonian systems. II. Zbl 0855.58030
Xu, Junxiang; Qiu, Qingjiu; You, Jiangong
1996
Persistence of the non-twist torus in nearly integrable Hamiltonian systems. Zbl 1202.37079
Xu, Junxiang; You, Jiangong
2010
On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s non-degeneracy condition. Zbl 1112.37046
Zhang, Dongfeng; Xu, Junxiang
2006
A KAM theorem of degenerate infinite dimensional Hamiltonian systems. I. Zbl 0855.58029
Xu, Junxiang; Qiu, Qingjiu; You, Jiangong
1996
On the reducibility of a class of nonlinear quasi-periodic system with small perturbation parameter near zero equilibrium point. Zbl 1151.34030
Wang, Xiaocai; Xu, Junxiang
2008
Existence of multiple positive solutions for Schrödinger-Poisson systems with critical growth. Zbl 1329.35144
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2015
Existence of multi-bump solutions for a semilinear Schrödinger-Poisson system. Zbl 1301.35159
Wang, Jun; Xu, Junxiang; Zhang, Fubao; Chen, Xumei
2013
Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Rüssmann’s non-degeneracy condition. Zbl 1102.37040
Zhang, Dongfeng; Xu, Junxiang
2006
On quasi-periodic solutions for a generalized Boussinesq equation. Zbl 1339.37078
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2014
Existence and multiplicity of solutions for a generalized Choquard equation. Zbl 1375.35134
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2017
Persistence of lower dimensional tori for a class of nearly integrable reversible systems. Zbl 1223.37075
Wang, Xiaocai; Zhang, Dongfeng; Xu, Junxiang
2011
Existence and multiplicity of solutions for superlinear fractional Schrödinger equations in $$\mathbb{R}^{N}$$. Zbl 1328.35225
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2015
On quasi-periodic perturbations of hyperbolic-type degenerate equilibrium point of a class of planar systems. Zbl 1278.34045
Xu, Junxiang
2013
On the reducibility of two-dimensional linear quasi-periodic systems with small parameter. Zbl 1352.37070
Xu, Junxiang; Lu, Xuezhu
2015
Positive ground states for asymptotically periodic Schrödinger-Poisson systems. Zbl 1271.35022
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2013
Existence of solutions for nonperiodic superquadratic Hamiltonian elliptic systems. Zbl 1183.35115
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2010
On invariant tori of vector field under weaker non-degeneracy condition. Zbl 1358.37101
Zhang, Dongfeng; Xu, Junxiang
2015
On a class of semilinear Schrödinger equations with indefinite linear part. Zbl 1312.35105
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2014
Invariant curves of analytic reversible mappings under Brjuno-Rüssmann’s non-resonant condition. Zbl 1320.47009
Zhang, Dongfeng; Xu, Junxiang
2014
On reducibility of linear differential equations with almost-periodic coefficients. Zbl 0922.34040
Xu, Junxiang; You, Jiangong
1996
A note on the extension of the Dinaburg-Sinai theorem to higher dimension. Zbl 1087.34023
Liang, Jianli; Xu, Junxiang
2005
Homoclinic orbits for superlinear Hamiltonian systems without Ambrosetti-Rabinowitz growth condition. Zbl 1203.37103
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2010
Ground state solutions for asymptotically periodic Schrödinger equations with indefinite linear part. Zbl 1317.35024
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2015
On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems. Zbl 1333.37091
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2016
Existence and multiplicity of solutions for asymptotically Hamiltonian elliptic systems in $$\mathbb R^N$$. Zbl 1187.35055
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2010
General KAM theorems and their applications to invariant tori with prescribed frequencies. Zbl 1344.37070
Xu, Junxiang; Lu, Xuezhu
2016
Persistence of elliptic lower dimensional invariant tori for small perturbation of degenerate integrable Hamiltonian systems. Zbl 0889.58045
Xu, Junxiang
1997
Existence of semiclassical ground-state solutions for semilinear elliptic systems. Zbl 1329.35141
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2012
On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters. Zbl 1350.34039
Xu, Junxiang; Kun, Wang; Min, Zhu
2016
Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing. Zbl 1366.37138
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2017
Persistence of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings. Zbl 1339.37044
Bi, Qiaoyan; Xu, Junxiang
2014
Reducibility of three dimensional skew symmetric system with Liouvillean basic frequencies. Zbl 1430.34052
Zhang, Dongfeng; Xu, Junxiang; Xu, Xindong
2018
Existence of infinitely many homoclinic orbits for nonperiodic superquadratic Hamiltonian systems. Zbl 1248.34055
Wang, Jun; Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2012
On the Cauchy problem for the two-component $$b$$-family system. Zbl 1277.35136
Zhu, Min; Xu, Junxiang
2013
Double crises in two-parameter forced oscillators by generalized cell mapping digraph method. Zbl 1098.70538
Hong, L.; Xu, J. X.
2003
On invariant tori with prescribed frequency in Hamiltonian systems. Zbl 1364.70034
Zhang, Dongfeng; Xu, Junxiang; Wu, Hao
2016
Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth. Zbl 1300.35033
Zhang, Hui; Xu, Junxiang; Zhang, Fubao; Du, Miao
2014
Persistence of invariant torus in Hamiltonian systems with two-degree of freedom. Zbl 1134.37025
Zhang, Li; Xu, Junxiang
2008
Erratum to: Existence and concentration of positive solutions for semilinear Schrödinger-Poisson systems in $${\mathbb{R}^{3}}$$. Zbl 1278.35073
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2013
On the quasi-periodic solutions for generalized Boussinesq equation with higher order nonlinearity. Zbl 1331.35176
Shi, Yanling; Xu, Junxiang; Xu, Xindong; Jiang, Shunjun
2015
An iterative method of point mapping under cell reference for the global analysis of non-linear dynamical systems. Zbl 1232.70041
Jiang, J.; Xu, J.-X
1996
On the reducibility for a class of quasi-periodic Hamiltonian systems with small perturbation parameter. Zbl 1222.37049
Li, Jia; Xu, Junxiang
2011
On reference governor in iterative learning control for dynamic systems with input saturation. Zbl 1228.93066
Tan, Y.; Xu, J. X.; Norrlöf, M.; Freeman, C.
2011
Homoclinic orbits for an unbounded superquadratic Hamiltonian systems. (Homoclinic orbits for an unbounded superquadratic.) Zbl 1202.58015
Wang, Jun; Xu, Junxiang; Zhang, Fubao; Wang, Lei
2010
Infinitely many homoclinic orbits for superlinear Hamiltonian systems. Zbl 1261.37026
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2012
Existence and nonexistence of the ground state solutions for nonlinear Schrödinger equations with nonperiodic nonlinearities. Zbl 1256.35143
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2012
Multiplicity of semiclassical states for Schrödinger-Poisson systems with critical frequency. Zbl 1433.35065
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2020
On the effective reducibility of a class of quasi-periodic Hamiltonian systems. Zbl 1332.34077
Li, Jia; Xu, Junxiang
2015
On small perturbations of a nonlinear periodic system with degenerate equilibrium. Zbl 1315.37038
Lu, Xuezhu; Xu, Junxiang
2014
Corrigendum for the paper “Invariant tori for nearly integrable Hamiltonian systems with degeneracy”. Zbl 1129.34314
Xu, Junxiang; You, Jiangong
2007
Periodic solutions for a class of non-autonomous differential delay equations. Zbl 1186.34091
Cheng, Rong; Xu, Junxiang
2009
A KAM theorem for a class of nearly integrable symplectic mappings. Zbl 1370.37117
Lu, Xuezhu; Li, Jia; Xu, Junxiang
2017
Bound and ground states for a concave-convex generalized Choquard equation. Zbl 06737056
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2017
Persistence of lower dimensional hyperbolic tori for reversible system. Zbl 1334.37068
Kong, Yuedong; Xu, Junxiang
2014
Distributed adaptive iterative learning control for nonlinear multiagent systems with state constraints. Zbl 1383.93004
Shen, D.; Xu, J.-X.
2017
Existence and concentration of positive ground state solutions for Schrödinger-Poisson systems. Zbl 1295.35219
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2013
Existence of positive ground states for some nonlinear Schrödinger systems. Zbl 1282.35363
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2013
Persistence of Floquet invariant tori for a class of non-conservative dynamical systems. Zbl 1189.37066
Xu, Junxiang
2007
Infinitely many solutions for diffusion equations without symmetry. Zbl 1231.35095
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2011
A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems. Zbl 1338.37075
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2016
Invariant tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s nondegeneracy condition. Zbl 1121.37046
Zhang, Dongfeng; Xu, Junxiang
2007
A new KAM iteration with nearly infinitely small steps in reversible systems of polynomial character. Zbl 1392.37048
Zhang, Dongfeng; Xu, Junxiang; Wang, Xiaocai
2018
Existence of positive and sign-changing solutions to a coupled elliptic system with mixed nonlinearity growth. Zbl 1448.35210
Wang, Jun; Xu, Junxiang
2020
On the reducibility of linear quasi-periodic systems with Liouvillean basic frequencies and multiple eigenvalues. Zbl 1475.70016
Zhang, Dongfeng; Xu, Junxiang; Wu, Hao; Xu, Xindong
2020
Solutions of super linear Dirac equations with general potentials. Zbl 1242.47055
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2009
The existence of solutions for superquadratic Hamiltonian elliptic systems on $$\mathbb R^N$$. Zbl 1204.35084
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2011
A symplectic map and its application to the persistence of lower dimensional invariant tori. Zbl 1099.37045
Xu, Junxiang; You, Jiangong
2002
Existence and multiplicity of semiclassical solutions for a Schrödinger equation. Zbl 1173.35695
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2009
Analysis of structural response under blast loads using the coupled SPH-FEM approach. Zbl 1152.74052
Xu, Junxiang; Liu, Xila
2008
Recovering strange attractors from noisy interspike intervals of neuronal firings. Zbl 0934.92005
Gong, Y. F.; Ren, W.; Shi, X. Z.; Xu, J. X.; Hu, S. J.
1999
Even homoclinic orbits for super quadratic Hamiltonian systems. Zbl 1201.37096
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2010
Multiple positive solutions for Kirchhoff type problems involving concave and convex nonlinearities in $$\mathbb R^3$$. Zbl 1353.35005
Cao, Xiaofei; Xu, Junxiang; Wang, Jun
2016
Quasi-periodic solutions for Schrödinger equation with derivative nonlinearity $$(|u|^{2p}u)_x$$. Zbl 1314.37055
Shi, Yanling; Lu, Xuezhu; Xu, Junxiang; Xu, Xindong
2015
Invariant tori with prescribed frequency for nearly integrable Hamiltonian systems. Zbl 1345.70027
Lu, Xuezhu; Xu, Junxiang
2014
Boundedness of solutions for a class of second-order differential equations. Zbl 1139.34033
Cheng, Chunrui; Xu, Junxiang
2008
On the persistence of elliptic lower-dimensional tori in Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition. Zbl 1114.37033
Wang, Shaoping; Zhang, Dongfeng; Xu, Junxiang
2007
A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems. Zbl 1364.37131
Zhang, Dongfeng; Xu, Junxiang; Wang, Xiaocai
2017
Reducibility of a class of nonlinear quasi-periodic systems with Liouvillean basic frequencies. Zbl 1469.37048
Zhang, Dongfeng; Xu, Junxiang
2021
Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems. Zbl 1481.37067
Xu, Junxiang; You, Jiangong
2020
On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity. Zbl 1308.76041
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2015
Quasi-periodic solutions for a class of higher dimensional beam equation with quasi-periodic forcing. Zbl 1411.37062
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2019
Homoclinic orbits of nonperiodic super quadratic Hamiltonian system. Zbl 1192.37088
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2010
Research on the periodic orbit of non-linear dynamic systems using Chebyshev polynomials. Zbl 1237.70084
Zhou, T.; Xu, J. X.; Chen, C. L.
2001
Reducibility of a class of nonlinear quasi-periodic systems with Liouvillean basic frequencies. Zbl 1469.37048
Zhang, Dongfeng; Xu, Junxiang
2021
Multiplicity of semiclassical states for Schrödinger-Poisson systems with critical frequency. Zbl 1433.35065
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2020
Existence of positive and sign-changing solutions to a coupled elliptic system with mixed nonlinearity growth. Zbl 1448.35210
Wang, Jun; Xu, Junxiang
2020
On the reducibility of linear quasi-periodic systems with Liouvillean basic frequencies and multiple eigenvalues. Zbl 1475.70016
Zhang, Dongfeng; Xu, Junxiang; Wu, Hao; Xu, Xindong
2020
Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems. Zbl 1481.37067
Xu, Junxiang; You, Jiangong
2020
Quasi-periodic solutions for a class of higher dimensional beam equation with quasi-periodic forcing. Zbl 1411.37062
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2019
Reducibility of three dimensional skew symmetric system with Liouvillean basic frequencies. Zbl 1430.34052
Zhang, Dongfeng; Xu, Junxiang; Xu, Xindong
2018
A new KAM iteration with nearly infinitely small steps in reversible systems of polynomial character. Zbl 1392.37048
Zhang, Dongfeng; Xu, Junxiang; Wang, Xiaocai
2018
Normalized solutions for a coupled Schrödinger system with saturable nonlinearities. Zbl 1382.35262
Cao, Xiaofei; Xu, Junxiang; Wang, Jun; Zhang, Fubao
2018
Existence and multiplicity of solutions for a generalized Choquard equation. Zbl 1375.35134
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2017
Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing. Zbl 1366.37138
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2017
A KAM theorem for a class of nearly integrable symplectic mappings. Zbl 1370.37117
Lu, Xuezhu; Li, Jia; Xu, Junxiang
2017
Bound and ground states for a concave-convex generalized Choquard equation. Zbl 06737056
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2017
Distributed adaptive iterative learning control for nonlinear multiagent systems with state constraints. Zbl 1383.93004
Shen, D.; Xu, J.-X.
2017
A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems. Zbl 1364.37131
Zhang, Dongfeng; Xu, Junxiang; Wang, Xiaocai
2017
The existence of solutions with prescribed $$L^{2}$$-norm for Kirchhoff type system. Zbl 1371.35056
Cao, Xiaofei; Xu, Junxiang; Wang, Jun
2017
Semiclassical ground states for a class of nonlinear Kirchhoff-type problems. Zbl 1379.35127
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2017
On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems. Zbl 1333.37091
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2016
General KAM theorems and their applications to invariant tori with prescribed frequencies. Zbl 1344.37070
Xu, Junxiang; Lu, Xuezhu
2016
On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters. Zbl 1350.34039
Xu, Junxiang; Kun, Wang; Min, Zhu
2016
On invariant tori with prescribed frequency in Hamiltonian systems. Zbl 1364.70034
Zhang, Dongfeng; Xu, Junxiang; Wu, Hao
2016
A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems. Zbl 1338.37075
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2016
Multiple positive solutions for Kirchhoff type problems involving concave and convex nonlinearities in $$\mathbb R^3$$. Zbl 1353.35005
Cao, Xiaofei; Xu, Junxiang; Wang, Jun
2016
Existence and nonexistence of ground states for a class of quasilinear Schrödinger equations. Zbl 1357.35109
Zhang, Hui; Zhang, Fubao; Xu, Junxiang
2016
On the persistence of degenerate lower-dimensional tori in reversible systems. Zbl 1351.37231
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2015
Existence of multiple positive solutions for Schrödinger-Poisson systems with critical growth. Zbl 1329.35144
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2015
Existence and multiplicity of solutions for superlinear fractional Schrödinger equations in $$\mathbb{R}^{N}$$. Zbl 1328.35225
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2015
On the reducibility of two-dimensional linear quasi-periodic systems with small parameter. Zbl 1352.37070
Xu, Junxiang; Lu, Xuezhu
2015
On invariant tori of vector field under weaker non-degeneracy condition. Zbl 1358.37101
Zhang, Dongfeng; Xu, Junxiang
2015
Ground state solutions for asymptotically periodic Schrödinger equations with indefinite linear part. Zbl 1317.35024
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2015
On the quasi-periodic solutions for generalized Boussinesq equation with higher order nonlinearity. Zbl 1331.35176
Shi, Yanling; Xu, Junxiang; Xu, Xindong; Jiang, Shunjun
2015
On the effective reducibility of a class of quasi-periodic Hamiltonian systems. Zbl 1332.34077
Li, Jia; Xu, Junxiang
2015
Quasi-periodic solutions for Schrödinger equation with derivative nonlinearity $$(|u|^{2p}u)_x$$. Zbl 1314.37055
Shi, Yanling; Lu, Xuezhu; Xu, Junxiang; Xu, Xindong
2015
On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity. Zbl 1308.76041
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2015
Multiple positive solutions for semilinear Schrödinger equations with critical growth in $$\mathbb{R}^{N}$$. Zbl 1318.35111
Wang, Jun; Lu, Dianchen; Xu, Junxiang; Zhang, Fubao
2015
KAM tori for defocusing modified KDV equation. Zbl 1375.37164
Shi, Yanling; Xu, Junxiang
2015
On quasi-periodic solutions for a generalized Boussinesq equation. Zbl 1339.37078
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2014
On a class of semilinear Schrödinger equations with indefinite linear part. Zbl 1312.35105
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2014
Invariant curves of analytic reversible mappings under Brjuno-Rüssmann’s non-resonant condition. Zbl 1320.47009
Zhang, Dongfeng; Xu, Junxiang
2014
Persistence of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings. Zbl 1339.37044
Bi, Qiaoyan; Xu, Junxiang
2014
Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth. Zbl 1300.35033
Zhang, Hui; Xu, Junxiang; Zhang, Fubao; Du, Miao
2014
On small perturbations of a nonlinear periodic system with degenerate equilibrium. Zbl 1315.37038
Lu, Xuezhu; Xu, Junxiang
2014
Persistence of lower dimensional hyperbolic tori for reversible system. Zbl 1334.37068
Kong, Yuedong; Xu, Junxiang
2014
Invariant tori with prescribed frequency for nearly integrable Hamiltonian systems. Zbl 1345.70027
Lu, Xuezhu; Xu, Junxiang
2014
Ground states for Schrödinger-Poisson systems with three growth terms. Zbl 1315.35088
Zhang, Hui; Zhang, Fubao; Xu, Junxiang
2014
Existence and concentration of positive solutions for semilinear Schrödinger-Poisson systems in $${\mathbb{R}^{3}}$$. Zbl 1278.35074
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2013
Existence of multi-bump solutions for a semilinear Schrödinger-Poisson system. Zbl 1301.35159
Wang, Jun; Xu, Junxiang; Zhang, Fubao; Chen, Xumei
2013
On quasi-periodic perturbations of hyperbolic-type degenerate equilibrium point of a class of planar systems. Zbl 1278.34045
Xu, Junxiang
2013
Positive ground states for asymptotically periodic Schrödinger-Poisson systems. Zbl 1271.35022
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2013
On the Cauchy problem for the two-component $$b$$-family system. Zbl 1277.35136
Zhu, Min; Xu, Junxiang
2013
Erratum to: Existence and concentration of positive solutions for semilinear Schrödinger-Poisson systems in $${\mathbb{R}^{3}}$$. Zbl 1278.35073
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2013
Existence and concentration of positive ground state solutions for Schrödinger-Poisson systems. Zbl 1295.35219
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2013
Existence of positive ground states for some nonlinear Schrödinger systems. Zbl 1282.35363
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2013
Wave-breaking phenomena and global solutions for periodic two-component Dullin-Gottwald-Holm systems. Zbl 1288.35125
Zhu, Min; Xu, Junxiang
2013
Ground state solutions for asymptotically periodic Schrödinger equations with critical growth. Zbl 1291.35040
Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2013
Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth. Zbl 1402.35119
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2012
On the wave-breaking phenomena for the periodic two-component Dullin-Gottwald-Holm system. Zbl 1298.35121
Zhu, Min; Xu, Junxiang
2012
Degenerate lower dimensional tori in reversible systems. Zbl 1260.37029
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2012
Existence of semiclassical ground-state solutions for semilinear elliptic systems. Zbl 1329.35141
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2012
Existence of infinitely many homoclinic orbits for nonperiodic superquadratic Hamiltonian systems. Zbl 1248.34055
Wang, Jun; Zhang, Hui; Xu, Junxiang; Zhang, Fubao
2012
Infinitely many homoclinic orbits for superlinear Hamiltonian systems. Zbl 1261.37026
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2012
Existence and nonexistence of the ground state solutions for nonlinear Schrödinger equations with nonperiodic nonlinearities. Zbl 1256.35143
Wang, Jun; Tian, Lixin; Xu, Junxiang; Zhang, Fubao
2012
Homoclinic orbits for a class of Hamiltonian systems with superquadratic or asymptotically quadratic potentials. Zbl 1231.37033
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2011
Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation. Zbl 1218.34050
Xu, Junxiang; Jiang, Shunjun
2011
On small perturbation of two-dimensional quasi-periodic systems with hyperbolic-type degenerate equilibrium point. Zbl 1217.34076
Xu, Junxiang
2011
Persistence of lower dimensional tori for a class of nearly integrable reversible systems. Zbl 1223.37075
Wang, Xiaocai; Zhang, Dongfeng; Xu, Junxiang
2011
On the reducibility for a class of quasi-periodic Hamiltonian systems with small perturbation parameter. Zbl 1222.37049
Li, Jia; Xu, Junxiang
2011
On reference governor in iterative learning control for dynamic systems with input saturation. Zbl 1228.93066
Tan, Y.; Xu, J. X.; Norrlöf, M.; Freeman, C.
2011
Infinitely many solutions for diffusion equations without symmetry. Zbl 1231.35095
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2011
The existence of solutions for superquadratic Hamiltonian elliptic systems on $$\mathbb R^N$$. Zbl 1204.35084
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2011
Lagrangian stability of a class of second-order periodic systems. Zbl 1222.34047
Jiang, Shunjun; Xu, Junxiang; Zhang, Fubao
2011
Existence and multiplicity of homoclinic orbits for the second order Hamiltonian systems. Zbl 1204.37067
Wang, Jun; Zhang, Fubao; Xu, Junxiang
2010
Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems. Zbl 1202.37080
Wang, Xiaocai; Xu, Junxiang; Zhang, Dongfeng
2010
Persistence of the non-twist torus in nearly integrable Hamiltonian systems. Zbl 1202.37079
Xu, Junxiang; You, Jiangong
2010
Existence of solutions for nonperiodic superquadratic Hamiltonian elliptic systems. Zbl 1183.35115
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2010
Homoclinic orbits for superlinear Hamiltonian systems without Ambrosetti-Rabinowitz growth condition. Zbl 1203.37103
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2010
Existence and multiplicity of solutions for asymptotically Hamiltonian elliptic systems in $$\mathbb R^N$$. Zbl 1187.35055
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2010
Homoclinic orbits for an unbounded superquadratic Hamiltonian systems. (Homoclinic orbits for an unbounded superquadratic.) Zbl 1202.58015
Wang, Jun; Xu, Junxiang; Zhang, Fubao; Wang, Lei
2010
Even homoclinic orbits for super quadratic Hamiltonian systems. Zbl 1201.37096
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2010
Homoclinic orbits of nonperiodic super quadratic Hamiltonian system. Zbl 1192.37088
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2010
On the existence of periodic solutions for a class of non-autonomous differential delay equations. Zbl 1209.34084
Cheng, Rong; Xu, Junxiang; Zhang, Dongfeng
2010
Solutions of non-periodic super-quadratic Dirac equations. Zbl 1186.35171
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2010
Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann’s non-degeneracy condition. Zbl 1175.37065
Wang, Xiaocai; Xu, Junxiang
2009
Periodic solutions for a class of non-autonomous differential delay equations. Zbl 1186.34091
Cheng, Rong; Xu, Junxiang
2009
Solutions of super linear Dirac equations with general potentials. Zbl 1242.47055
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2009
Existence and multiplicity of semiclassical solutions for a Schrödinger equation. Zbl 1173.35695
Wang, Jun; Xu, Junxiang; Zhang, Fubao
2009
Existence of homoclinic orbits for Hamiltonian systems with superquadratic potentials. Zbl 1187.37086
Ding, Jian; Xu, Junxiang; Zhang, Fubao
2009
On invariant curves of analytic reversible mappings with degeneracy. Zbl 1180.37084
Zhang, Dongfeng; Xu, Junxiang
2009
On the reducibility of a class of nonlinear quasi-periodic system with small perturbation parameter near zero equilibrium point. Zbl 1151.34030
Wang, Xiaocai; Xu, Junxiang
2008
Persistence of invariant torus in Hamiltonian systems with two-degree of freedom. Zbl 1134.37025
Zhang, Li; Xu, Junxiang
2008
Analysis of structural response under blast loads using the coupled SPH-FEM approach. Zbl 1152.74052
Xu, Junxiang; Liu, Xila
2008
Boundedness of solutions for a class of second-order differential equations. Zbl 1139.34033
Cheng, Chunrui; Xu, Junxiang
2008
Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann’s non-degeneracy condition. Zbl 1112.37045
Xu, Junxiang; You, Jiangong
2007
Corrigendum for the paper “Invariant tori for nearly integrable Hamiltonian systems with degeneracy”. Zbl 1129.34314
Xu, Junxiang; You, Jiangong
2007
Persistence of Floquet invariant tori for a class of non-conservative dynamical systems. Zbl 1189.37066
Xu, Junxiang
2007
Invariant tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s nondegeneracy condition. Zbl 1121.37046
Zhang, Dongfeng; Xu, Junxiang
2007
On the persistence of elliptic lower-dimensional tori in Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition. Zbl 1114.37033
Wang, Shaoping; Zhang, Dongfeng; Xu, Junxiang
2007
Invariant curves of smooth quasi-periodic reversible mappings. Zbl 1142.37342
Zhang, Dongfeng; Xu, Junxiang
2007
On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s non-degeneracy condition. Zbl 1112.37046
Zhang, Dongfeng; Xu, Junxiang
2006
Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Rüssmann’s non-degeneracy condition. Zbl 1102.37040
Zhang, Dongfeng; Xu, Junxiang
2006
...and 17 more Documents
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### Cited by 552 Authors

 69 Xu, Junxiang 31 Tang, Xianhua 28 Zhang, Fubao 25 Zhang, Dongfeng 24 Wang, Jun 16 Li, Yong 13 Geng, Jiansheng 13 Shi, Yanling 13 Zhang, Hui 13 Zhang, Wen 12 Ma, Shiwang 12 Xu, XinDong 11 Si, Jianguo 11 You, Jiangong 10 Liu, Zhisu 10 Wang, Xiaocai 10 Xie, Qilin 10 Zhang, Jian 10 Zhang, Ziheng 9 Ambrosio, Vincenzo 9 Chen, Guanwei 9 Chen, Haibo 8 Chen, Sitong 8 Li, Gongbao 8 Yi, Yingfei 8 Zhang, Jianjun 8 Zhao, Fukun 7 Guo, Shangjiang 7 Jiang, Shunjun 7 Si, Wen 7 Sun, Juntao 7 Wang, Dabin 7 Xiao, Lu 7 Ye, Hongyu 6 Alves, Claudianor Oliveira 6 Chen, Jianqing 6 Cheng, Bitao 6 Cong, Fuzhong 6 Figueiredo, Giovany Malcher 6 Guan, Wen 6 Huang, Yisheng 6 Lei, Chunyu 6 Li, Quanqing 6 Lü, Dengfeng 6 Lu, Xuezhu 6 Shi, Junping 6 Shuai, Wei 6 Teng, Kaimin 6 Yuan, Rong 5 Du, Miao 5 Li, Fuyi 5 Liu, Zeng 5 Peng, Shuangjie 5 Qin, Dongdong 5 Santos, João R. jun. 5 Sevryuk, Mikhail Borisovich 5 Suo, Hong-Min 5 Tian, Lixin 5 Wang, Wenbo 5 Wu, Tsungfang 4 Chen, Peng 4 Chu, Changmu 4 Hanßmann, Heinz 4 He, Xiaoming 4 Li, Yuhua 4 Liao, Jiafeng 4 Qian, Weichao 4 Wu, Xian 4 Wu, Yuanze 4 Yang, Xue 4 Ye, Yiwei 4 Yu, Jian-She 4 Yu, Yuanyang 4 Zhu, Chunpeng 3 Cao, Xiaofei 3 Chen, Shaowei 3 Cheng, Rong 3 Do Ó, João M. Bezerra 3 Gao, Meina 3 Germano, Geilson F. 3 Grigoryan, Gevorg Avagovich 3 Guo, Zhengguang 3 Han, Yuecai 3 Han, Zhiqing 3 He, Yi 3 Hu, Tingxi 3 Jia, HuiFang 3 Kong, Yuedong 3 Li, Lin 3 Li, Xinfu 3 Liao, Fangfang 3 Liu, Chungen 3 Liu, Gaosheng 3 Liu, Jiu 3 Liu, Shujuan 3 Lu, Lu 3 Mao, Anmin 3 Minhós, Feliz Manuel 3 Nieto Roig, Juan Jose 3 Ren, Xiufang ...and 452 more Authors
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### Cited in 119 Serials

 46 Journal of Differential Equations 43 Journal of Mathematical Analysis and Applications 40 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Journal of Mathematical Physics 25 Communications on Pure and Applied Analysis 20 Boundary Value Problems 18 Computers & Mathematics with Applications 18 Mathematical Methods in the Applied Sciences 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 18 Discrete and Continuous Dynamical Systems 16 Journal of Dynamics and Differential Equations 15 Applicable Analysis 13 Nonlinear Analysis. Real World Applications 12 Advances in Difference Equations 11 Qualitative Theory of Dynamical Systems 10 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 9 Abstract and Applied Analysis 9 Complex Variables and Elliptic Equations 8 Acta Mathematica Sinica. English Series 7 Applied Mathematics and Computation 7 Monatshefte für Mathematik 7 Applied Mathematics Letters 7 Topological Methods in Nonlinear Analysis 7 Calculus of Variations and Partial Differential Equations 7 Advanced Nonlinear Studies 6 Proceedings of the American Mathematical Society 6 Dynamical Systems 6 Discrete and Continuous Dynamical Systems. Series B 6 Mediterranean Journal of Mathematics 6 Advances in Nonlinear Analysis 5 Mathematische Nachrichten 5 The Journal of Geometric Analysis 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Journal of Inequalities and Applications 5 Regular and Chaotic Dynamics 5 Communications in Contemporary Mathematics 5 Annales Henri Poincaré 5 Journal of Applied Mathematics and Computing 5 Journal of Function Spaces 4 Chaos, Solitons and Fractals 4 Acta Applicandae Mathematicae 4 Electronic Journal of Differential Equations (EJDE) 4 NoDEA. Nonlinear Differential Equations and Applications 3 Indian Journal of Pure & Applied Mathematics 3 Nonlinearity 3 Rocky Mountain Journal of Mathematics 3 Ergodic Theory and Dynamical Systems 3 Journal of Nonlinear Science 3 Frontiers of Mathematics in China 3 Journal of Nonlinear Science and Applications 3 Science China. Mathematics 3 Journal of Applied Analysis and Computation 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Archiv der Mathematik 2 Duke Mathematical Journal 2 Journal of Functional Analysis 2 Transactions of the American Mathematical Society 2 Chinese Annals of Mathematics. Series B 2 Asymptotic Analysis 2 Science in China. Series A 2 Indagationes Mathematicae. New Series 2 Potential Analysis 2 Discrete Dynamics in Nature and Society 2 Communications in Nonlinear Science and Numerical Simulation 2 Milan Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Advances in Mathematical Physics 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Analysis and Mathematical Physics 2 SN Partial Differential Equations and Applications 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Lithuanian Mathematical Journal 1 Ukrainian Mathematical Journal 1 Acta Mathematica Vietnamica 1 Advances in Mathematics 1 Annales Polonici Mathematici 1 Glasgow Mathematical Journal 1 Manuscripta Mathematica 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Quaestiones Mathematicae 1 Results in Mathematics 1 Studies in Applied Mathematics 1 Physica D 1 Journal of the Ramanujan Mathematical Society 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Mathematical Sciences (New York) 1 Turkish Journal of Mathematics 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Nonlinear Dynamics 1 Positivity 1 Taiwanese Journal of Mathematics ...and 19 more Serials
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### Cited in 24 Fields

 409 Partial differential equations (35-XX) 219 Dynamical systems and ergodic theory (37-XX) 94 Ordinary differential equations (34-XX) 93 Mechanics of particles and systems (70-XX) 44 Global analysis, analysis on manifolds (58-XX) 26 Operator theory (47-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 15 Quantum theory (81-XX) 8 Mechanics of deformable solids (74-XX) 8 Fluid mechanics (76-XX) 4 Integral equations (45-XX) 4 Differential geometry (53-XX) 3 Real functions (26-XX) 3 Numerical analysis (65-XX) 2 Number theory (11-XX) 2 Difference and functional equations (39-XX) 2 Algebraic topology (55-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Functional analysis (46-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)