Banach function spaces and exponential instability of evolution families

Mihail Megan, Adina Luminita Sasu and Bogdan Sasu

Address.
Department of Mathematics,
Faculty of Mathematics and Computer Science
 West University of Timisoara
Bul. V. Parvan, Nr. 4, 1900 - Timisoara, Romania

E-mail:  megan@hilbert.math.uvt.ro      sasu@hilbert.math.uvt.ro

Abstract.
In this paper we give necessary and sufficient conditions for
uniform exponential instability of evolution families in Banach
spaces, in terms of Banach function spaces.
 Versions of some well-known theorems due to Datko,
Neerven, Rolewicz  and Zabczyk, are obtained for the case of uniform
 exponential instability of evolution families.

AMSclassification.    34E05,  34D05

Keywords.   Evolution family, uniform exponential instability, Banach function spaces.