On Uniform Polynomial Stability of Variational Nonautonomous Difference Equations in Banach Spaces

Tomescu, Mihaela Aurelia

doi:10.2478/awutm-2013-0020

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On Uniform Polynomial Stability of Variational Nonautonomous Difference Equations in Banach Spaces

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 51 (2013): Issue 2 (December 2013)

By: Mihaela Aurelia Tomescu

Open Access

|Jan 2014

Abstract

In this paper we give characterizations for uniform polynomial stability property of variational nonautonomous difference equations. We obtain results that generalize the well-known theorems due to R.Datko ([3]), E.Barbashin ([1]) and A.Lyapunov ([4]) for variational nonautonomous difference equations.

References

[1] E. A. Barbashin, Introduction in Stability Theory, Izd. Nauka, Moskva, 1967.
Search in Google Scholar
[2] L. Barreira and C. Valls, Polynomial growth rates, Nonlinear Analysis, 7, (2009), 5208-5219.10.1016/j.na.2009.04.005
Search in Google Scholar
[3] R. Datko, Uniform asymptotic stability of evolutionary processes in a Banach spaces, SIAM J.Math. Anal., 3, (1973), 428-455.10.1137/0503042
Search in Google Scholar
[4] A. Lyapunov, The General Problem of the Stability of Motion, Taylor end Francis, 1992.10.1080/00207179208934253
Search in Google Scholar
[5] M. Megan, T. Ceauşu, and M. L. Rămneanţu, Polynomial stability of evolution operators in Banach spaces, Opuscula Mathematica, 31/2, (2011), 279-288.10.7494/OpMath.2011.31.2.279
Search in Google Scholar
[6] M. Megan, T. Ceauşu, and M. A. Tomescu, On exponential stability of variational nonautonomous difference equations in Banach spaces, Ann. Acad. Rom. Sci, Ser. Math. Appl., 4/1, (2012), 20-31.10.1155/2013/407958
Search in Google Scholar
[7] M. Megan and C. Stoica, Discrete asymptotic behaviors for skew-evolution semiows on Banach spaces, Carpathian J. Math., 24, (2008), 348-355.
Search in Google Scholar