On Uniform Exponential Dichotomy of Evolution Operators

Mihai Gabriel Babuţia; Traian Ceausu; Nicolae Marian Seimeanu

doi:10.2478/v10324-012-0011-6

.blurhash-client-img { display: none !important; }

On Uniform Exponential Dichotomy of Evolution Operators

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 50 (2012): Issue 2 (December 2012)

By: Mihai Gabriel Babuţia, Traian Ceausu and Nicolae Marian Seimeanu

Open Access

|Jan 2013

Abstract

The present paper presents three distinct concepts of uniform exponential dichotomy for evolution operators in Banach spaces. Characterizations and relationships between them and some illustrative counterexamples are given.

References

[1] L. Barreira and C. Valls, Stability of Nonautonomous Dierential Equations, Lecture Notes in Mathematics 1926, 200810.1007/978-3-540-74775-8
Search in Google Scholar
[2] C. Chicone and Y Latushkin, Evolution Semigroups in Dynamical Systems and Diferential Equations, Math. Surveys and Monographs, vol. 70, Amer. Math. Soc., 199910.1090/surv/070
Search in Google Scholar
[3] W. A. Coppel, Stability and asymptotic behaviour of diferential equations, D.C. Heath, Boston, 1965
Search in Google Scholar
[4] J. L. Daleckii and M. G. Krein, Stability of diferential equations in Banach space, Amer. Math. Soc., Providence, R. I., 1974
Search in Google Scholar
[5] J. L. Massera and J. J. Schafer, Linear diferential equations and function spaces, Academic Press, New York and London, 1966
Search in Google Scholar
[6] M. Megan, On (h,k)-dichotomy of evolution operators in Banach spaces, Dynamic Systems and Applications, 5, (1996), 189-196
Search in Google Scholar
[7] M. Megan, B. Sasu, and A. L. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces, Integral Equations Operator Theory, 44, (2002), 71-7810.1007/BF01197861
Search in Google Scholar
[8] N. Van Minh, F. Rabiger, and R. Schnaubelt, Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half-line, Integr. Equ. Oper. Theory, 32, (1998), 332-35310.1007/BF01203774
Search in Google Scholar
[9] O. Perron, Die stabilitatsfrage bei Diferentialgleischungen, Math. Z., 32, (1930), 703-72810.1007/BF01194662
Search in Google Scholar
[10] P. Preda and M. Megan, Exponential dichotomy of evolutionary processes in Banach spaces, Czechoslovak Mathematical Journal, 35 (2), (1985), 312-32310.21136/CMJ.1985.102019
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10324-012-0011-6 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

Journal RSS Feed

Language: English

Page range: 3 - 14

Published on: Jan 15, 2013

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

exponential dichotomy,

evolution operator.

Related subjects:

Mathematics,

General mathematics

© 2013 Mihai Gabriel Babuţia, Traian Ceausu, Nicolae Marian Seimeanu, published by West University of Timisoara
This work is licensed under the Creative Commons License.

Volume 50 (2012): Issue 2 (December 2012)