Dynamics of Solutions and Approximation for Partial Functional Differential Equations with Delay

Abstract

This work aims to investigate the existence and uniqueness of almost periodic solution for partial functional differential equations with delay. Here, we assume that the undelayed part is not necessarily densely defined and satisfies the well-known Hille–Yosida condition, the delayed parts are assumed to be almost periodic with respect to the first argument and Lipschitz continuous with respect to the second argument. Using the exponential dichotomy and the contraction mapping principle, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution.