带有偏差变元的广义 Hamilton系统周期解的存在性(英文)

On the Existence of Periodic Solutions to Generalized Hamiltonian Systems with Delays

应用变分方法与 Morse理论 ,本文讨论下面含有时滞的广义 Hamilton系统的周期解 ,J* dudt=g(t,u(t-r1) ,… ,u(t-rs) )其中 J*是非奇异 2 n× 2 n反对称矩阵 .在一定条件下 ,本文得到上述方程至少存在两个非平凡 2 π-周期解 ;而对于一般的微分系统 ,本文给出其具有变分结构的判定性准则 .

In this paper,we consider the following generalized retarded Hamiltonian systems, J* du dt=g(t,u(t-r1) ,… ,u(t-rs) ) and obtain the existence of nontrival 2π-periodic solutions by using Morse theory. As a general rule,we also discuss the feature of differential systems with variational structure.