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The Scientific World Journal
Volume 2013 (2013), Article ID 793813, 8 pages
http://dx.doi.org/10.1155/2013/793813
Research Article

Trichotomy for Dynamical Systems in Banach Spaces

Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, 2 Elena Drăgoi Str, 310330 Arad, Romania

Received 25 July 2013; Accepted 13 August 2013

Academic Editors: G. Bonanno, F. Minhós, and G.-Q. Xu

Copyright © 2013 Codruţa Stoica. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept of -trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sustained by several examples.