Instabilit\'{e} des cocycles d'\'{e}volution fortement mesurables dans des espaces de Banach

TL;DR

This paper investigates various long-term behaviors of skew-evolution semiflows in Banach spaces, including stability and instability, and establishes new criteria and relations among these properties using a unified nonuniform approach.

Contribution

It introduces two Datko type theorems and provides a comprehensive nonuniform framework for analyzing asymptotic behaviors of skew-evolution semiflows.

Findings

Proves two new Datko type theorems.

Establishes relations between different asymptotic behaviors.

Provides a unified nonuniform approach for stability analysis.

Abstract

The aim of the paper is to present various asymptotic behaviors of skew-evolution semiflows in Banach spaces, as exponential decay, instability, exponential in- stability and integral instability. Relations between these asymptotic properties are also given. As main results, two Datko type theorems are proved. A unified nonuniform approach is provided.