Weighted pseudo-almost periodic solutions for some neutral partial functional differential equations

Abstract

In this article we study the existence of weighted pseudo almost periodic solutions of an autonomous neutral functional differential equation with Stepanov-Weighted pseudo almost periodic terms in a Banach space. We use the contraction mapping principle to show the existence and the uniqueness of weighted pseudo almost periodic solution of the equation.

Keywords

• Neutral equation
• semigroup
• mild solution
• Stepanov-weighted pseudo almost periodic functions
• Banach fixed point theorem