一类具有多个偏差变元的二阶中立型泛函微分方程的周期解

Periodic Solutions for A Kind of Second-order Neutral Functional Differential Equation with Multiple Deviating Arguments

利用重合度理论,获得了一类具有多个偏差变元的二阶中立型泛函微分方程(d^2)/(dt^2)(u(t)-(sum from j=1 to n)c_ju(t-r_j))=f(u(t))u′(t)+α(t)g(u(t))+(sum from j=1 to n)β_j(t)g(u(t-γ_j(t)))+p(t)周期解存在性的新的充分条件,改进了已有文献的相关结果.

By using a continuation theorem based on coincidence degree theory and inequality technique, some new sufficient conditions of periodic solutions are established for second-order neutral functional differential equation with multiple deviating arguments as follows d^2/dt^2（u（t）-∑ j=1^ncju（t-rj））=f（u（t））u′（t）＋α（t）g（u（t））＋∑ j=1^nβj（t）g（u（t-rj（t）））＋p（t） The results have improved the related reports in the literatures.