Li, Tao; Llibre, Jaume Limit cycles in piecewise polynomial Hamiltonian systems allowing nonlinear switching boundaries. (English) Zbl 1511.34016 J. Differ. Equations 344, 405-438 (2023). Reviewer: Zhengdong Du (Chengdu) MSC: 34A36 34C07 34C29 34C05 37J46 34C23 34E10 PDFBibTeX XMLCite \textit{T. Li} and \textit{J. Llibre}, J. Differ. Equations 344, 405--438 (2023; Zbl 1511.34016) Full Text: DOI
Guo, Zhifei; Llibre, Jaume Limit cycles of a class of discontinuous piecewise differential systems separated by the curve \(y= x^n\) via averaging theory. (English) Zbl 1510.34049 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 12, Article ID 2250187, 19 p. (2022). Reviewer: Zhengdong Du (Chengdu) MSC: 34C05 34A30 34C29 34E10 34C07 34C23 PDFBibTeX XMLCite \textit{Z. Guo} and \textit{J. Llibre}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 12, Article ID 2250187, 19 p. (2022; Zbl 1510.34049) Full Text: DOI
Guo, Zhifei; Llibre, Jaume Non-equivalence between the Melnikov and the averaging methods for nonsmooth differential systems. (English) Zbl 1506.34028 Qual. Theory Dyn. Syst. 21, No. 4, Paper No. 114, 13 p. (2022). Reviewer: Fabio Vito Difonzo (Bari) MSC: 34A36 34C29 34C05 34E10 PDFBibTeX XMLCite \textit{Z. Guo} and \textit{J. Llibre}, Qual. Theory Dyn. Syst. 21, No. 4, Paper No. 114, 13 p. (2022; Zbl 1506.34028) Full Text: DOI
Euzébio, Rodrigo D.; Llibre, Jaume; Tonon, Durval J. Lower bounds for the number of limit cycles in a generalised Rayleigh-Liénard oscillator. (English) Zbl 1509.34035 Nonlinearity 35, No. 8, 3883-3906 (2022). Reviewer: Alexander Grin (Grodno) MSC: 34C07 34C05 34C23 34C37 34E10 34B30 PDFBibTeX XMLCite \textit{R. D. Euzébio} et al., Nonlinearity 35, No. 8, 3883--3906 (2022; Zbl 1509.34035) Full Text: DOI arXiv
Liu, Changjian; Li, Chengzhi; Llibre, Jaume The cyclicity of the period annulus of a reversible quadratic system. (English) Zbl 1508.34030 Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 2, 281-290 (2022). Reviewer: Jeidy Johana Jimenez (Goiânia) MSC: 34C07 34C08 34C23 34E10 34C14 34C05 PDFBibTeX XMLCite \textit{C. Liu} et al., Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 2, 281--290 (2022; Zbl 1508.34030) Full Text: DOI Link
Chen, Xingwu; Li, Tao; Llibre, Jaume Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications. (English) Zbl 1495.34026 J. Differ. Equations 314, 340-369 (2022). Reviewer: Dingheng Pi (Quanzhou) MSC: 34A36 34C07 34C05 34C23 34C29 34E10 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Differ. Equations 314, 340--369 (2022; Zbl 1495.34026) Full Text: DOI
Li, Tao; Llibre, Jaume Limit cycles of piecewise polynomial differential systems with the discontinuity line \(xy = 0\). (English) Zbl 1490.34038 Commun. Pure Appl. Anal. 20, No. 11, 3887-3909 (2021). Reviewer: Armengol Gasull (Barcelona) MSC: 34C07 34E10 34A36 34C05 34C23 34C14 34C29 37J40 PDFBibTeX XMLCite \textit{T. Li} and \textit{J. Llibre}, Commun. Pure Appl. Anal. 20, No. 11, 3887--3909 (2021; Zbl 1490.34038) Full Text: DOI
Llibre, Jaume; Novaes, Douglas D.; Rodrigues, Camila A. B. Bifurcations from families of periodic solutions in piecewise differential systems. (English) Zbl 1500.34031 Physica D 404, Article ID 132342, 12 p. (2020). MSC: 34C25 37C60 34C45 34C29 34C23 34E10 34A36 PDFBibTeX XMLCite \textit{J. Llibre} et al., Physica D 404, Article ID 132342, 12 p. (2020; Zbl 1500.34031) Full Text: DOI arXiv
Cardoso, João L.; Llibre, Jaume; Novaes, Douglas D.; Tonon, Durval J. Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields. (English) Zbl 1479.34057 Dyn. Syst. 35, No. 3, 490-514 (2020). Reviewer: Xiuli Cen (Zhuhai) MSC: 34C05 34C07 34C23 34A36 34E10 PDFBibTeX XMLCite \textit{J. L. Cardoso} et al., Dyn. Syst. 35, No. 3, 490--514 (2020; Zbl 1479.34057) Full Text: DOI arXiv
Garcia, Antonio; Llibre, Jaume Existence of periodic solutions for a class of second order ordinary differential equations. (English) Zbl 1494.34119 Acta Appl. Math. 169, 193-197 (2020). Reviewer: Manuel Zamora (Concepción) MSC: 34C25 34C29 34E10 37C60 PDFBibTeX XMLCite \textit{A. Garcia} and \textit{J. Llibre}, Acta Appl. Math. 169, 193--197 (2020; Zbl 1494.34119) Full Text: DOI Link
Llibre, Jaume; Martínez, Paulina; Vidal, Claudio Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin. (English) Zbl 1451.34033 Can. Math. Bull. 63, No. 3, 547-561 (2020). MSC: 34C07 34C08 34E10 PDFBibTeX XMLCite \textit{J. Llibre} et al., Can. Math. Bull. 63, No. 3, 547--561 (2020; Zbl 1451.34033) Full Text: DOI
Llibre, Jaume; Novaes, Douglas D.; Zeli, Iris O. Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems. (English) Zbl 1441.34029 Rev. Mat. Iberoam. 36, No. 1, 291-318 (2020). Reviewer: Jihua Yang (Guyuan) MSC: 34A36 34C05 34C29 34C23 34E10 37C60 PDFBibTeX XMLCite \textit{J. Llibre} et al., Rev. Mat. Iberoam. 36, No. 1, 291--318 (2020; Zbl 1441.34029) Full Text: DOI arXiv
Llibre, Jaume; Tang, Yilei Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. (English) Zbl 1478.34040 Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1769-1784 (2019). Reviewer: Stefano Marò (Pisa) MSC: 34C07 34C29 34C25 34C05 34A36 34E10 34C23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{Y. Tang}, Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1769--1784 (2019; Zbl 1478.34040) Full Text: DOI arXiv
Itikawa, Jackson; Llibre, Jaume; Novaes, Douglas Duarte A new result on averaging theory for a class of discontinuous planar differential systems with applications. (English) Zbl 1386.34081 Rev. Mat. Iberoam. 33, No. 4, 1247-1265 (2017). MSC: 34C29 34C07 34C25 34A36 34C23 34E10 PDFBibTeX XMLCite \textit{J. Itikawa} et al., Rev. Mat. Iberoam. 33, No. 4, 1247--1265 (2017; Zbl 1386.34081) Full Text: DOI
Colak, Ilker E.; Llibre, Jaume; Valls, Claudia On the bifurcation of limit cycles due to polynomial perturbations of Hamiltonian centers. (English) Zbl 1375.34063 Mediterr. J. Math. 14, No. 2, Paper No. 40, 10 p. (2017). Reviewer: Jaume Giné (Lleida) MSC: 34C23 34C05 34E10 34C07 37J45 PDFBibTeX XMLCite \textit{I. E. Colak} et al., Mediterr. J. Math. 14, No. 2, Paper No. 40, 10 p. (2017; Zbl 1375.34063) Full Text: DOI Link
Llibre, Jaume; Valls, Claudia Limit cycles for a variant of a generalized Riccati equation. (English) Zbl 1361.34031 Appl. Math. Lett. 68, 76-79 (2017). MSC: 34C07 34A34 34C08 34E10 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Appl. Math. Lett. 68, 76--79 (2017; Zbl 1361.34031) Full Text: DOI Link
Llibre, Jaume; Rodrigues, Ana A non-autonomous kind of Duffing equation. (English) Zbl 1328.34034 Appl. Math. Comput. 251, 669-674 (2015). MSC: 34C25 34E10 34C29 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{A. Rodrigues}, Appl. Math. Comput. 251, 669--674 (2015; Zbl 1328.34034) Full Text: DOI Link
Llibre, Jaume; Novaes, Douglas D.; Teixeira, Marco A. Limit cycles bifurcating from the periodic orbits of a discontinuous piecewise linear differentiable center with two zones. (English) Zbl 1327.34067 Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 11, Article ID 1550144, 11 p. (2015). MSC: 34C23 34E10 34A36 34C05 PDFBibTeX XMLCite \textit{J. Llibre} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 11, Article ID 1550144, 11 p. (2015; Zbl 1327.34067) Full Text: DOI
Buică, Adriana; Giné, Jaume; Llibre, Jaume Periodic solutions for nonlinear differential systems: the second- order bifurcation function. (English) Zbl 1360.34089 Topol. Methods Nonlinear Anal. 43, No. 2, 403-419 (2014). MSC: 34C25 34C29 34E10 34C20 34C23 PDFBibTeX XMLCite \textit{A. Buică} et al., Topol. Methods Nonlinear Anal. 43, No. 2, 403--419 (2014; Zbl 1360.34089) Full Text: DOI
Llibre, Jaume; Valls, Claudia On the number of limit cycles for a generalization of Liénard polynomial differential systems. (English) Zbl 1270.34052 Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 3, Article ID 1350048, 16 p. (2013). MSC: 34C07 34C05 34C23 34C29 34E10 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 3, Article ID 1350048, 16 p. (2013; Zbl 1270.34052) Full Text: DOI
Ferragut, Antoni; Llibre, Jaume; Pantazi, Chara Polynomial vector fields in \(\mathbb R^3\) with infinitely many limit cycles. (English) Zbl 1270.34041 Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 2, Article ID 1350029, 10 p. (2013). MSC: 34C05 34E10 PDFBibTeX XMLCite \textit{A. Ferragut} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 2, Article ID 1350029, 10 p. (2013; Zbl 1270.34041) Full Text: DOI
Buică, Adriana; Giné, Jaume; Llibre, Jaume A second order analysis of the periodic solutions for nonlinear periodic differential systems with a small parameter. (English) Zbl 1247.34060 Physica D 241, No. 5, 528-533 (2012). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C25 34C29 34E10 PDFBibTeX XMLCite \textit{A. Buică} et al., Physica D 241, No. 5, 528--533 (2012; Zbl 1247.34060) Full Text: DOI Link
Llibre, J.; Novaes, D. D.; Teixeira, M. A. On the periodic solutions of a perturbed double pendulum. (English) Zbl 1272.34051 São Paulo J. Math. Sci. 5, No. 2, 317-330 (2011). MSC: 34C25 34C29 70E17 34E10 PDFBibTeX XMLCite \textit{J. Llibre} et al., São Paulo J. Math. Sci. 5, No. 2, 317--330 (2011; Zbl 1272.34051) Full Text: DOI arXiv
Li, Chengzhi; Llibre, Jaume Quadratic perturbations of a quadratic reversible Lotka-Volterra system. (English) Zbl 1213.34071 Qual. Theory Dyn. Syst. 9, No. 1-2, 235-249 (2010). Reviewer: Gheorghe Tigan (Timisoara) MSC: 34E10 34C07 34C08 34C05 34C23 34C14 PDFBibTeX XMLCite \textit{C. Li} and \textit{J. Llibre}, Qual. Theory Dyn. Syst. 9, No. 1--2, 235--249 (2010; Zbl 1213.34071) Full Text: DOI
Buică, A.; Llibre, J.; Makarenkov, O. Yu. On Yu. A. Mitropol’skii’s theorem on periodic solutions of systems of nonlinear differential equations with nondifferentiable right-hand sides. (English. Russian original) Zbl 1221.34108 Dokl. Math. 78, No. 1, 525-527 (2008); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 3, 302-304 (2008). MSC: 34C25 34C29 34E10 PDFBibTeX XMLCite \textit{A. Buică} et al., Dokl. Math. 78, No. 1, 525--527 (2008; Zbl 1221.34108); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 3, 302--304 (2008) Full Text: DOI arXiv
García, Belén; Llibre, Jaume; Pérez del Río, Jesús S. On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree. (English) Zbl 1361.34030 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 12, 4461-4469 (2008). MSC: 34C07 34C23 37G15 34C29 34C05 34E10 PDFBibTeX XMLCite \textit{B. García} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 12, 4461--4469 (2008; Zbl 1361.34030) Full Text: DOI
Buică, Adriana; Llibre, Jaume Limit cycles of a perturbed cubic polynomial differential center. (English) Zbl 1298.34061 Chaos Solitons Fractals 32, No. 3, 1059-1069 (2007). MSC: 34C07 34C05 34C23 34E10 PDFBibTeX XMLCite \textit{A. Buică} and \textit{J. Llibre}, Chaos Solitons Fractals 32, No. 3, 1059--1069 (2007; Zbl 1298.34061) Full Text: DOI
Giacomini, Hector; Llibre, Jaume; Viano, Mireille On the shape of limit cycles that bifurcate from Hamiltonian centers. (English) Zbl 0954.34022 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 41, No. 3-4, 523-537 (2000). Reviewer: Klaus R.Schneider (Berlin) MSC: 34C05 34C23 37G15 37K50 34E10 37K55 PDFBibTeX XMLCite \textit{H. Giacomini} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 41, No. 3--4, 523--537 (2000; Zbl 0954.34022) Full Text: DOI