Local theory for retarded equations with infinite delay^∗

^∗Supposed by the National Ntural Science Foundation of China

Abstract

The purpose of this paper is to establish local theory for retarded functional differential equations with infinite delay, Some new conditions are proposed, and new results are obtained which is more general than the previous one. Our phase space is pseudo-metric space. We do not need x₊ to be continuous in t on phase space. Our theorems are especially effective for Volterra integro-differential equations

Keywords:

• Functional differential equation
• infinite delay
• phase space
• local theory
• Volterra equation

^∗Supposed by the National Ntural Science Foundation of China

^∗Supposed by the National Ntural Science Foundation of China

Notes

^∗Supposed by the National Ntural Science Foundation of China