摘要
研究非自治的二阶Hamilton系统:±ü=▽F(t,u(t)),a.e.t∈[0,T],u(0)-u(T)=■(0)-■(T)=0的周期解.当位势函数是一个(λ,μ)次凸函数与一个次二次函数的和时,利用极小作用原理和鞍点定理得到了非平凡周期解存在的几个充分条件.更全面地讨论了含有(λ,μ)次凸位势的Hamilton系统的周期解,推广和补充了某些已知的结果.
The non-autonomous second order Hamiltonian systems：±ü=△↓F（t,u（t））,a.e.t∈[0,T],u（0）-u（T）=u^·（0）-u^·（T）=0 have been studied.The problems with potentials being the sums of（λ,μ） subconvex functions and subquadratic functions are considered by the least action principle and the saddle point theorem.Some sufficient conditions for nontrivial periodic solutions are obtained.Periodic solutions of Hamiltonian systems with（λ,μ） subconvex potentials are discussed comprehensively.The results provide a generalization and complement for some known ones.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2009年第1期181-184,共4页
Journal of Southeast University：Natural Science Edition
关键词
周期解
非自治Hamilton系统
极小作用原理
鞍点定理
periodic solutions
non-autonomous Hamiltonian systems
the least action principle
saddle point theorem
