带双参数的脉冲泛函微分方程正周期解的存在性

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

研究了带双参数的脉冲泛函微分方程u'(t)=h(t,u(t))-λf(t,u(t-τ(t))),t∈R,t≠tk,u(t+k)-u(tk)=μIk(tk,u(tk-τ(tk)))正周期解的存在性,其中λ>0,μ≥0为参数,获得了其在更一般条件下正周期解的存在性结果。主要结果的证明基于不动点指数理论。

We study the existence of positive periodic solutions of impulsive functional differential equations with two parameters u＇（t）=h（t,u（t））-λf（t,u（t-τ（t）））,t∈R,t≠tk,u（t＋k）-u（tk）=μIk（tk,u（tk-τ（tk）））,where λ〉0,μ≥0 are parameters and show the existence results of positive periodic solutions in more general condi- tions. The proof of the main results is based on the fixed point index theory.