Abstract:

The concept of weak exponential instability for evolution families in Banach spaces is presented. Some property of weak exponential expansiveness for evolution families and the necessary and sufficient conditions concerning the weak exponential instability are given in Banach spaces. Variants of Datko result for weak exponential instability of a well-known result from is obtained in the stability theory.

Key words: evolution families, weak exponential instability, uniform exponential instability