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Stability for retarded functional differential equations

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Abstract

It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations are obtained by means of the correspondence of this class of equations with GODEs.

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Authors and Affiliations

  1. Institute of Mathematics Sciences and Computer Science, University of São Paulo, São Carlos, Brazil

    M. Federson

  2. Mathematical Institute, Academy of Sciences of Czech Republic, Prague, Czech Republic

    Š. Schwabik

Authors
  1. M. Federson
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  2. Š. Schwabik
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 107–126, January, 2008.

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Federson, M., Schwabik, Š. Stability for retarded functional differential equations. Ukr Math J 60, 121–140 (2008). https://doi.org/10.1007/s11253-008-0047-2

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  • DOI: https://doi.org/10.1007/s11253-008-0047-2

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