Lipschitz stability of generalized ordinary differential equations and impulsive retarded differential equations

Afonso, Suzete M. and da Silva, Márcia R.: Lipschitz stability of generalized ordinary differential equations and impulsive retarded differential equations. Electronic journal of qualitative theory of differential equations 18. pp. 1-18. (2019)

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Abstract

We consider a class of retarded functional differential equations with preassigned moments of impulsive effect and we study the Lipschitz stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals. We introduce the concept of variational Lipschitz stability and Lipschitz stability for generalized ordinary differential equations and we develop the theory in this direction by establishing conditions for the trivial solutions of generalized ordinary differential equations to be variationally Lipschitz stable. Thereby, we apply the results to get the corresponding ones for impulsive functional differential equations.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 18
Page Range: pp. 1-18
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.18
Uncontrolled Keywords: Differenciálegyenlet - retardált, Differenciálegyenlet
Additional Information: Bibliogr.: 18. p. ; összefoglalás angol nyelven
Date Deposited: 2019. May. 31. 05:53
Last Modified: 2019. May. 31. 05:53
URI: http://acta.bibl.u-szeged.hu/id/eprint/58099

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