Let be a locally compact metric space and a Banach space. A mapping is called a semiflow if it is continuous and such that
Let be a semiflow on and let be a continuous mapping satisfying some extra conditions (for example, – the identity operator on ; for and . The pair is called linear strongly continuous skew-product semiflow on . A strongly continuous skew-product semiflow is called uniformly exponentially stable if there exist and such that for and .
Moreover, the authors used the concept that a pair of Schäffer spaces is admissible to . The main result of the paper asserts that is uniformly exponentially stable if and only if there exists a pair of Schäffer spaces admissible to and satisfying some additional condition. This nice paper contains also some other results and interesting examples explaining the basic concepts and illustrating the obtained results.