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Exponential dichotomy of evolution operators in Banach spaces

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Optimization, Optimal Control and Partial Differential Equations

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Abstract

This paper introduces a concept of exponential dichotomy for a general class of nonlinear evolution operators. Necessary and sufficient conditions for exponential dichotomy are given. Obtained results are generalizations of well-known results of R. Datko (1973) and A. Ichikawa (1984) about exponential stability.

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References

  • Coppel W. A. (1978), Dichotomies in Stability Theory, Lecture Notes in Mathematics, Nr. 629, Springer-Verlag, Berlin.

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  • Datko R. (1973), Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space, SIAM J. Math. Anal., pp. 428-445.

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  • Ichikawa A. (1984), Equivalence of Lp Stability and Exponential Stability for a Class of Nonlinear Semigroups, Nonlinear Analysis Theory, Methods and Applications, vol. 8, nr. 9, pp. 805–815.

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  • Massera J.L., Schaffer J.J.(1966), Linear Differential Equations and Function Spaces, Acad. Press, New York and London

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  • Preda P., Megan M. (1985), Exponential Dichotomy of Evolutionary Processes in Banach Spaces, Czechosl. Math. Journal, vol. 35(110), pp.312–323.

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Author information

Authors and Affiliations

  1. Departament of Mathematics, University of Timisoara, Bul. V. Parvan Nr. 4, 1900, Timisoara, Romania

    Mihail Megan & Radu Latcu

Authors
  1. Mihail Megan
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  2. Radu Latcu
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Editor information

Editors and Affiliations

  1. Faculty of Mathematics, University of Iasi, Bld Copou 11, 6600, Iasi, Romania

    Viorel Barbu

  2. Institute of Mathematics, Romanian Academy of Science, Bld Pacii 212, 79622, Bucharest, Romania

    Dan Tiba

  3. INRIA-Rocquencourt, Domaine de Voluceau, BP 105, 78153, Le Chesnay Cedex, France

    J. Frédéric Bonnans

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© 1992 Springer Basel AG

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Megan, M., Latcu, R. (1992). Exponential dichotomy of evolution operators in Banach spaces. In: Barbu, V., Tiba, D., Bonnans, J.F. (eds) Optimization, Optimal Control and Partial Differential Equations. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 107. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8625-3_5

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  • DOI: https://doi.org/10.1007/978-3-0348-8625-3_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9704-4

  • Online ISBN: 978-3-0348-8625-3

  • eBook Packages: Springer Book Archive

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