zbMATH — the first resource for mathematics

On radial solutions for Monge-Ampère equations. (English) Zbl 1438.35202
Summary: In this paper, we obtain some new existence, uniqueness, and multiplicity results of radial solutions of an elliptic system coupled by Monge-Ampère equations using the fixed point theorem.
35J96 Monge-Ampère equations
47N20 Applications of operator theory to differential and integral equations
35B07 Axially symmetric solutions to PDEs
Full Text: DOI
[1] Caffarelli L, Nirenberg L, Spruck J. The Dirichlet problem for nonlinear second-order elliptic equations I. MongeAmpère equations. Comm Pure Appl Math 1984; 37: 369-402. · Zbl 0598.35047
[2] Gao M, Wang F. Existence of convex solutions for systems of Monge-Ampère equations. Bound Value Probl 2015; 2015: 128.
[3] Goncalves J, Santos C. Classical solutions of singular Monge-Ampère equation in a ball. J Math Anal Appl 2005; 305: 240-252. · Zbl 1141.35373
[4] Guo D, Lakshmikantham V. Nonlinear problems in abstract cones. New York, NY, USA: Academic Press, 1988. · Zbl 0661.47045
[5] Gutierrez C. The Monge-Ampère Equation. Basel, Switzerland: Birkhauser, 2000.
[6] Hu S, Wang H. Convex solutions of boundary value problems arising from Monge-Ampère equations. Discrete Contin Dyn Syst 2006; 16: 705-720. · Zbl 1121.34027
[7] Kutev N. Nontrivial solutions for the equations of Monge-Ampère type. J Math Anal Appl 1988; 132: 424-433. · Zbl 0658.35035
[8] Liang Z, Chu J. Radially symmetric convex solutions for Dirichlet problems of Monge-Ampère equations. Math Meth Appl Sci 2016; 39: 3426-3433. · Zbl 1359.34034
[9] Lions P. Two remarks on Monge-Ampère equations. Ann Mat Pura Appl 1985; 142: 263-275. · Zbl 0594.35023
[10] Mohammed A. Singular boundary value problems for the Monge-Ampère equation. Nonlinear Anal 2009; 70: 457464.
[11] Qi Z, Zhang Z. On a power-type coupled system of Monge-Ampère equations. Topol Methods Nonlinear Anal 2015; 46: 717-729. · Zbl 1366.35055
[12] Wang H. Convex solutions of boundary value problems. J Math Anal Appl 2006; 318: 246-252. · Zbl 1099.34023
[13] Wang H. Convex solutions of systems arising from Monge-Ampère equations. Electron J Qual Theory Differ Equ. 2009, Special Edition I, No. 26, 8 pp.
[14] Wang H. Convex solutions of systems of Monge-Ampère equations. arXiv:1007. 3013v2 [math.AP].
[15] Wang F, An Y. Triple nontrivial radial convex solutions of systems of Monge-Ampère equations. Appl Math Lett 2012; 25: 88-92. · Zbl 1233.35106
[16] Wang F, Sun S. Existence and multiplicity of positive solutions for singular Monge-Ampère equations. Bull Iranian Math Soc 2015; 41: 1387-1399. · Zbl 1373.34044
[17] Zhang Z, Wang K. Existence and non-existence of solutions for a class of Monge-Ampère equations. J Differ Equations 2009; 246: 2849-2875. · Zbl 1165.35023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.