二阶脉冲中立型泛函微分方程周期解的存在性

Existence of Periodic Solutions for Second Order Neutral Functional Differential Equation with Impulses

利用重合度理论研究了在脉冲条件下二阶非线性脉冲中立型泛函微分方程[x(t)+cx(t-τ)]″=f(t,x(t-σ)),t>t0,t≠tkΔx(tk)=gk(x(tk)),Δx′(tk)=hk(x′(tk)),k=1,2…的周期解的存在性,得出了该周期解存在的充分条件。

By using the coincidence degree theory, the following second order nonlinear neutral functional differential equation with impulses is studied：[x（t）＋cx（t-τ）]＂=f（t,x（t-σ））, t〉t0,t≠tk△x（tk）=gk（x（tk））,△x＇（tk）=hk（x＇（tk））, k=1,2…. and a sufficient condition for existence of periodic solutions of this equation has been obtained.