Generalizations of a theorem of Rolewicz

Abstract

The aim of this article is to give a unified treatment for the theorems of Rolewicz and Neerven type for uniform exponential stability of evolution families. We obtain necessary and sufficient conditions for uniform exponential stability of evolution families, generalizing a stability theorem due to Rolewicz and we present a new proof for the Rolewicz theorem, based on the theory of Banach function spaces. Finally, we apply our results and we deduce a generalization for a classical stability theorem due to Przyluski and Rolewicz.

Keywords:

• Evolution family
• Uniform exponential stability
• AMS: 34 D05

Acknowledgements

The author would like to thank the referees for their suggestions and comments.

Notes

Email: [email protected]; [email protected]

Additional information

Notes on contributors

Bogdan Sasu *

Email: [email protected]; [email protected]