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Existence of periodic solutions for Hamiltonian systems with super-linear and sign-changing nonlinearities. (English) Zbl 1459.37054

Summary: In this paper, we consider the existence of periodic solutions for the super quadratic second order Hamiltonian system, and primitive functions of nonlinearities are allowed to be sign-changing. By using some weaker conditions, our result extends and improves some existed results in the literature.

MSC:

37J46 Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems
34C25 Periodic solutions to ordinary differential equations
37C27 Periodic orbits of vector fields and flows
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
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