一类非凸自治二阶Hamilton系统的极小周期解

THE MINIMAL PERIODIC SOLUTIONS OF A CLASS OF NONCONVEX AUTONOMOVS SECOND ORDER HAMILTONIAN SYSTEMS

本文通过比较泛函的极小临界点和平凡临界点的Ｍｏｒｓｅ指标，得到一个关于非凸自治二阶Ｈａｍｉｌｔｏｎ系统非常值极小周期解的存在性定理。

In this paper,by comparing the Morse indexes of the critical points corresponding to the minimal value and the trivial value of the variational function,the existence of the minimal periodic solutions for a class of nonconvex autonomous second order Hamiltonian systems are discussed.