Periodic solutions with prescribed minimal period to Hamiltonian systems

Journal of inequalities and applications

article

Huafeng Xiao¹  Zupei Shen² 

[1] School of Mathematics and Information Science, Guangzhou University;School of Financial Mathematics and Statistics, Guangdong University of Finance

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

DOI  :  10.1186/s13660-020-02524-4

学科分类：电力

来源: SpringerOpen

【 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.

【 授权许可】

CC BY