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2018 A continuation lemma and the existence of periodic solutions of perturbed planar Hamiltonian systems with sub-quadratic potentials
Zaihong Wang, Tiantian Ma
Topol. Methods Nonlinear Anal. 52(2): 693-706 (2018). DOI: 10.12775/TMNA.2018.037

Abstract

In this paper, we study the existence of periodic solutions of perturbed planar Hamiltonian systems of the form $$ \begin{cases} x'=f(y)+p_1(t,x,y), \\ y'=-g(x)+p_2(t,x,y). \end{cases} $$ We prove a continuation lemma for a given planar system and further use it to prove that this system has at least one $T$-periodic solution provided that $g$ has some sub-quadratic potentials.

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Zaihong Wang. Tiantian Ma. "A continuation lemma and the existence of periodic solutions of perturbed planar Hamiltonian systems with sub-quadratic potentials." Topol. Methods Nonlinear Anal. 52 (2) 693 - 706, 2018. https://doi.org/10.12775/TMNA.2018.037

Information

Published: 2018
First available in Project Euclid: 25 November 2018

zbMATH: 07051687
MathSciNet: MR3915658
Digital Object Identifier: 10.12775/TMNA.2018.037

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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