二阶哈密顿系统的同宿轨

Homoclinic Orbits of the Second-order Hamiltonian System

利用变分法和傅里叶分析,研究了当势函数满足一定条件时的二阶哈密顿系统同宿轨的存在性.传统的方法是利用山路引理,寻找鞍点型临界点来解决同宿轨的存在性.使用了不常用的变分直接方法,推广前人的结论,证明当势函数满足较弱的条件时同宿轨的存在性.

We use the calculus of variation and Fourier analysis to study the existence of homoclinic orbits of the second-order Hamiltonian systems when the potential function to meet certain conditions. The traditional method is to use the mountain pass,looking saddle point type critical point to address the existence of homoclinic orbits. In this paper,we use the direct method is not commonly used variational and we promote the previous conclusion. Finally,we prove the existence of homoclinic orbits when the potential function satisfies the conditions of weakness.