一阶带线性部分Hamilton系统的周期解

Periodic Solutions for the First Order Hamiltonian System with Linear Part

利用极小极大原理来研究一阶带线性部分Hamilton系统周期解的存在性与多重性问题.当线性部分正定时,在较弱的条件下,利用广义山路引理,得到系统至少有一个非常数周期解.此外,当位势函数是偶函数时,利用喷泉定理,得到系统有无穷多个非常数周期解.

In this paper,we consider the existence and multiplicity of periodic solutions for the first order Hamiltonian system with linear part by using the minimax methods.When the linear part is definite,under weaker condition than known ones,by using the generalized Mountain Pass Lemma,we obtain the system has at least one nonconstant periodic solution.Moreover,when the potential is even,by using the Fountain Theorem,we obtain that system has infinitely many nonconstant periodic solutions.