Almost automorphic delayed differential equations and Lasota-Wazewska model

TL;DR

This paper investigates the existence and uniqueness of almost automorphic solutions in abstract delayed differential equations, employing ergodicity, exponential dichotomy, and bi-almost automorphicity techniques.

Contribution

It provides new sufficient conditions for the existence and uniqueness of almost automorphic solutions in delayed differential equations, extending previous theoretical frameworks.

Findings

Established existence of almost automorphic solutions.

Provided conditions for uniqueness of solutions.

Applied ergodicity and exponential dichotomy methods.

Abstract

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of almost automorphic solutions are given.