On Exponential Stability for Skew-Evolution Semiflows on Banach Spaces

TL;DR

This paper investigates exponential stability of skew-evolution semiflows on Banach spaces, providing new characterizations and unifying uniform and nonuniform cases, including discrete time formulations.

Contribution

It introduces generalized stability criteria for skew-evolution semiflows, extending previous concepts and unifying uniform and nonuniform stability analyses.

Findings

Several general characterizations of exponential stability.

Unified treatment of uniform and nonuniform stability.

Discrete time stability results.

Abstract

The paper emphasizes the property of stability for skew-evolution semiflows on Banach spaces, defined by means of evolution semiflows and evolution cocycles and which generalize the concept introduced by us in a previous paper. There are presented several general characterizations of this asymptotic property out of which can be deduced well known results of the stability theory. A unified treatment in the uniform and in the nonuniform setting is given. The main results are also formulated in discrete time.