中立型标量积分微分方程的周期解(英文)

Periodic Solutions of Scalar Neutral Integro-Differential Equation

本文考虑中立型标量方程的周期的存在唯一性问题.其中a是连续函数,f是R×R 上的连续函数,g(l,s,x)和h(l,s,x)是R×R×R上的连续函数,以及a(l+T)=a(t),g(l+T,s+T,x)=g(l,s,x),h(l+T,s+T,x)=h(l,s,x),f(l+T,x)=f(l,x).通过利用线性系统解的估计式和泛函分析的方法,我们得到保证上述系统周期解存在和唯一的充分性条件.

This paper deals with the existence and uniqueness of periodic solutions of scalar neutral integro-differential equation with infinite delay of the form where a is continuous function , f is continuous function on R ×R , g (l ,s,x ) and h(l,s,z) are continuous functions on R×R×R, also a(t+T)=a(t), g (t+T , s+T ,x)=g (l,s,x) ,h(t+T , s+T , x) = h(t,s,x), f(l+T, x )=f(l,x). The sufficient conditions for the existing unique periodic solution of the equation are obtained by using functional analysis method and the estimated formulas of solutions of the linear scalar system.