ABSTRACT
STA BILITY METHODS FOR SEMILINEA R EVOLUTION EQUATIONS A ND NONLINEA R
EVOLUTION EQUATIONS
3 . 1 . SKEW PRODUCT FLOWS OF PROCESSES AND QUASI - PROCESSES AND STABILITY OF INTEGRALS
Let Y b e a nonempty closed set in X. We call the mapping w a y-quasi-process on X or simply a quasi-process on X, if w satisfies the condition ,
(p3) the restricted mapping w : R+ x R+ X Y I-t X is continuous ,
together with the conditions (pI ) and (p2) . In case of Y = X, the concept of quasi processes is identical with that of processes investigated in [53] , [54] [77] , [78] and [120] . We emphasize that the concept of processes does not fit in with the study of p-stabilities in functional differential equations in contrast with the concept of quasi-processes, as will be seen in Section 3.3 . The p-stability is a useful tool in the study of the existence of almost periodic solutions for almost periodic systems .
