Abstract. In this paper we consider a nonuniform unsrability concept for evolution operators in Banach spaces. The relationship between this concept and the Perron condition is studied. Generalizations to the nonuniform case of some results of Van Minh, Rabiger and Schnaubelt are obtained. The theory we present here is applicable for general time - varying linear equations in Banach spaces.
1991 Mathematics Subject Classification. 34D05, 34D20.
Key words and phrases. Evolution operator, exponential unstability, admissibility.