Stability for retarded functional differential equations |
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Authors: | M Federson Š Schwabik |
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Institution: | 1. Institute of Mathematics Sciences and Computer Science, University of S?o Paulo, S?o Carlos, Brazil 2. Mathematical Institute, Academy of Sciences of Czech Republic, Prague, Czech Republic
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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.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 107–126, January, 2008. |
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Keywords: | |
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