2006•Journal of Natural Science of Heilongjiang UniversityRequires access

The periodic solutions of a Volterra neutral integro-differential equation with infinite delay

Chang Run Xiao

Abstract

By using the matrix measure and exponential dichotomy,an operator T is created according to the equation discussed.The Schauder fixed point theorem is used to discuss the existence,uniqueness and uniform stability of periodic solutions for a class of Volterra Integro-differential system with infinite delayddt(x(t)-B(t,s)x(s)ds)=A(t)x(t)+∫~ ~t_-∞C(t,s)x(s)ds+f(t,x_t)The results obtained generalized and improved some known ones.

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Key concepts: Mathematics, Uniqueness, Fixed-point theorem, Differential equation, Volterra equations, Functional differential equation, Operator (biology), Class (philosophy)