On Exponential Stability of Variational Nonautonomous Difference Equations in Banach Spaces∗

In this paper we study two concepts of exponential stability for variational nonautonomous difference equations in Banach spaces. Characterizations of these concepts are given. The obtained results can be considered as generalizations for variational nonautonomous difference equations of some well-known theorems due to Barbashin and Datko . MSC: 34D05, 34D20, 93D20 keywords: variational difference equations, discrete skew-evolution semiflows, exponential stability ∗Accepted for publication on December 20, 2011. †[email protected] Academy of Romanian Scientists, Independenţei 54, Bucharest, 050094, Romania; West University of Timişoara, Department of Mathematics, Bd. V.Pârvan, Nr. 4, 300223, Timişoara, Romania; This work was partially supported from the Exploratory Research Grant PN II ID 1080 No. 508/2009 of the Romanian Ministry of Education, Research and Inovation ‡West University of Timişoara, Department of Mathematics, Bd. V.Parvan, Nr. 4, 300223, Timişoara, Romania §University of Petroşani, Department of Mathematics, University Street 20, 332006 Petroşani, Romania 20 Ann. Acad. Rom. Sci. Ser. Math. Appl. ISSN 2066 6594 Vol. 4, No. 1 / 2012 On exponential stability in Banach spaces 21