On the uniform exponential stability of linear skew‐product semiflows

Abstract

Abstract. The problem of uniform exponential stability of linear skew-product semiflows on locally compact metric space with Banach fibers, is discussed. It is established a connection between the uniform exponential stability of linear skewproduct semiflows and some admissibility-type condition. This approach is based on the method of "test functions", using a very large class of function spaces, the so-called Orlicz spaces.

A discrete-time approach in the qualitative theory of skew-product three-parameter semiflows

“…Other extensions of Perron's results for the infinite-dimensional Banach spaces were obtained by J. L. Daleckij, M. G. Krein [2], J. L. Massera, J.J Schäffer [9], [10] and N. van Minh, F. Räbiger, R. Schnaubelt [11]. Some other results concerning the property of stability for the (non)linear skewproduct three-parameter semiflows in the framework of infinite-dimensional Banach spaces were also obtained by C. Stoica, M. Megan [20], C. Preda, P. Preda, A. P. Petre [16] and P. V. Hai [3], [4]. Definition 2.1.…”

Polynomial expansiveness and admissibility of weighted Lebesgue spaces

“…We also refer the reader to paper [3] extending Ta Li's theorem to infinite-dimensional Banach spaces. Some different characterizations can be found in papers [2], [10], [16].…”