Criterion for exponential dichotomy of periodic generalized linear differential equations and an application to admissibility

TL;DR

This paper establishes a necessary and sufficient criterion for exponential dichotomy in periodic generalized linear differential equations, simplifying the understanding of admissibility in such systems.

Contribution

It introduces a new criterion for exponential dichotomy in periodic generalized linear systems, offering a simpler alternative to existing admissibility results.

Findings

Established a necessary and sufficient condition for exponential dichotomy.

Reformulated admissibility criteria with increased simplicity.

Enhanced understanding of periodic generalized linear differential equations.

Abstract

In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of admissibility, obtaining an alternative formulation with a particular simplicity.