Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions

TL;DR

This paper investigates a class of delay differential equations with infinite delay in weighted spaces, developing spectral theory and stability results including a Hopf bifurcation theorem for the associated semiflow.

Contribution

It introduces a spectral theory framework for infinite delay differential equations in weighted spaces and establishes local stability and bifurcation results.

Findings

Spectral theory for delay equations with infinite delay

Local stability conditions derived

Hopf bifurcation theorem established

Abstract

In this article we study a class of delay differential equations with infinite delay in weighted spaces of uniformly continuous functions. We focus on the integrated semigroup formulation of the problem and so doing we provide an spectral theory. As a consequence we obtain a local stability result and a Hopf bifurcation theorem for the semiflow generated by such a problem