On a class of differential-algebraic equations with infinite delay

TL;DR

This paper investigates the existence of periodic solutions in a class of differential-algebraic equations with infinite delay, transforming them into retarded functional differential equations on manifolds under certain conditions.

Contribution

It introduces a framework to analyze T-periodic solutions of perturbed DAE with infinite delay by converting them into retarded functional differential equations on manifolds.

Findings

Established conditions for the existence of T-periodic solutions.

Extended analysis to equations with distributed and infinite delay.

Linked DAE solutions to retarded functional differential equations.

Abstract

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed equations are equivalent to Retarded Functional (Ordinary) Differential Equations on a manifold. Our study is based on known results about the latter class of equations.