×

Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces. (English) Zbl 0831.34067

Authors’ abstract: “In this paper we introduce a concept of exponential dichotomy for skew-product semiflow in infinite dimensional Banach spaces which is an extension of the classic concept for evolution operators. This concept is used to study the roughness property of the skew-product semiflow. Also, we introduce the concept of discrete skew-product and give a necessary and sufficient condition for this discrete skew-product to have a discrete dichotomy. After that, we give necessary and sufficient conditions for the existence of exponential dichotomy for skew-product semiflow. Moreover we prove that the exponential dichotomy for skew-product semiflow is not destroyed by small perturbation. Finally, we apply these results to parabolic partial differential equations and functional differential equations”.

MSC:

34G20 Nonlinear differential equations in abstract spaces
34D05 Asymptotic properties of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI