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September  2006, 5(3): 551-569. doi: 10.3934/cpaa.2006.5.551

Input-output conditions for the asymptotic behavior of linear skew-product flows and applications

Bogdan Sasu 1, and  A. L. Sasu 2,

1. 

Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Blvd. No. 4, 300223 Timişoara, Romania
2. 

Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Bul. V. Pârvan Nr. 4, 300223-Timişoara, Romania

Received  June 2005 Revised  January 2006 Published  June 2006

In this paper we present a new approach concerning the uniform exponential dichotomy of linear skew-product flows and extend existing results on exponential dichotomy roughness for variational systems in infinite dimensional spaces. We introduce new concepts of admissibility and we deduce their connections with the uniform exponential dichotomy of discrete linear skew-product flows. We apply our results at the study of the exponential dichotomy roughness of discrete linear skew-product flows, presenting an estimation for the lower bound of the dichotomy radius.
Keywords: dichotomy radius., admissibility, Exponential dichotomy.
Mathematics Subject Classification: Primary: 34D09, Secondary: 39A11, 93D25, 46E3.
Citation: Bogdan Sasu, A. L. Sasu. Input-output conditions for the asymptotic behavior of linear skew-product flows and applications. Communications on Pure and Applied Analysis, 2006, 5 (3) : 551-569. doi: 10.3934/cpaa.2006.5.551
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