含反馈控制和参数的非线性泛函微分系统的正周期解的分析(英文)

Analysis of Positive Periodic Solutions of Nonlinear Functional Differential System with Feedback Control and a Parameter

我们研究下面具有反馈控制和参数的非线性微分系统的正周期解的存在性与不存在性:在一定条件下通过应用Leggett-Williams不动点定理,证明该系统至少有三个正周期解;在另外的条件下,通过用反证法证明了该系统的正周期解不存在.

We investigate the existence and nonexistence of positive periodic solutions of nonlinear differential system with feedback control and a parameter as follow：{dx/dt=-r（t）x（t）＋λF（t,xt,u（t-δ（t）））,du/dt=-h（t）u（t）＋g（t）x（t-σ（t））.In some sufficient conditions, by employing Leggett-Williams multiple fixed point theorem, we obtained at least three positive periodic solutions; In other some sufficient conditions, by using reduction to absurdity, we prove there is no positive periodic solution.