Periodic solutions with prescribed minimal period to Hamiltonian systems

[摘要] In this article, we study the existence of periodic solutions to second order Hamiltonian systems. Our goal is twofold. When the nonlinear term satisfies a strictly monotone condition, we show that, for any $T>0$ , there exists a T-periodic solution with minimal period T. When the nonlinear term satisfies a non-decreasing condition, using a perturbation technique, we prove a similar result. In the latter case, the periodic solution corresponds to a critical point which minimizes the variational functional on the Nehari manifold which is not homeomorphic to the unit sphere.

[学科分类] 电力

[关键词] Periodic solution;Hamiltonian systems;Nehari manifold;Perturbation technique;Minimal period