A continuation lemma and the existence of periodic solutions of perturbed planar Hamiltonian systems with sub-quadratic potentials
Keywords
Continuation lemma, sub-quadratic potential, periodic solutionAbstract
n 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.References
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Z. Wang and T. Ma, Periodic solutions of planar Hamiltonian systems with asymmetric nonlinearities, Boundary Value Problems, 2017, No. 46.
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