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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Barreira, Luis and Valls, Claudia 2016. Nonuniform exponential stability and admissibility. Linear and Multilinear Algebra, Vol. 64, Issue. 3, p. 440.


    Bento, António J.G. and Silva, César M. 2014. Nonuniform dichotomic behavior: Lipschitz invariant manifolds for ODEs. Bulletin des Sciences Mathématiques, Vol. 138, Issue. 1, p. 89.


    Lupa, Nicolae and Megan, Mihail 2014. Exponential dichotomies of evolution operators in Banach spaces. Monatshefte für Mathematik, Vol. 174, Issue. 2, p. 265.


    Jiang, Yongxin and Liao, Fang-fang 2012. Admissibility for Nonuniform(μ,ν)Contraction and Dichotomy. Abstract and Applied Analysis, Vol. 2012, p. 1.


    Preda, Ciprian Preda, Petre and Praţa, Cristina 2012. An extension of some theorems of L. Barreira and C. Valls for the nonuniform exponential dichotomous evolution operators. Journal of Mathematical Analysis and Applications, Vol. 388, Issue. 2, p. 1090.


    Valls, Claudia and Barreira, Luis 2012. Admissibility versus nonuniform exponential behavior for noninvertible cocycles. Discrete and Continuous Dynamical Systems, Vol. 33, Issue. 4, p. 1297.


    Barreira, Luís and Valls, Claudia 2011. Nonuniform exponential dichotomies and admissibility. Discrete and Continuous Dynamical Systems, Vol. 30, Issue. 1, p. 39.


    Barreira, Luis and Valls, Claudia 2010. Admissibility for nonuniform exponential contractions. Journal of Differential Equations, Vol. 249, Issue. 11, p. 2889.


    Stoica, Diana 2010. Uniform exponential dichotomy of stochastic cocycles. Stochastic Processes and their Applications, Vol. 120, Issue. 10, p. 1920.


    Amalia, Minda Andrea Mihaela, Tomescu Cornelia, Anghel and Diana, Stoica 2009. 2009 International Conference on Future Computer and Communication. p. 256.

    Tomescu, Mihaela Minda, Andrea Amalia Anghel, Cornelia Victoria and Popovici, Paraschiva 2009. 2009 International Conference on Signal Processing Systems. p. 976.

    Preda, P. and Megan, M. 1984. Exponential dichotomy of strongly discontinuous semigroups. Bulletin of the Australian Mathematical Society, Vol. 30, Issue. 03, p. 435.


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  • Bulletin of the Australian Mathematical Society, Volume 27, Issue 1
  • February 1983, pp. 31-52

Nonuniform dichotomy of evolutionary processes in Banach spaces

  • Petre Preda (a1) and Mihail Megan (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700011473
  • Published online: 01 April 2009
Abstract

In this paper we study nonuniform dichotomy concepts of linear evolutionary processes which are defined in a general Banach space and whose norms can increase no faster than an exponential. Connections between the dichotomy concepts and (B, D) admissibility properties are established. These connections have been partially accomplished in an earlier paper by the authors for the case when the process was a semigroup of class C0 and (B, D) = [(Lp, Lq).

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]W.A. Coppel , Dichotomies in stability theory (Lecture Notes in Mathematics, 629. Springer-Verlag, Berlin, Heidelberg, New York, 1978).

[2]Ruth Curtain and A.J. Pritchard , “The infinite-dimensional Riccati equation for systems defined by evolution operators”, SIAM J. Control Optim. 14 (1976), 951983.

[4]Mihail Megan , “On the input-output stability of linear controllable systems”, Canad. Math. Bull. 21 (1978), 187195.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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