Semigroups on Frechet spaces and equations with infinite delays

TL;DR

This paper establishes the existence and uniqueness of solutions for functional differential equations with infinite delay by selecting an appropriate Frechet space to encompass a broad class of initial functions.

Contribution

It introduces a novel approach using Frechet spaces to handle infinite delay in differential equations, ensuring solution existence and uniqueness.

Findings

Existence and uniqueness of solutions proven

Frechet space effectively handles infinite delay

Broad class of initial functions covered

Abstract

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.