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.
Citation
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