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

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 va...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations Vol. 2019; no. 18; pp. 1 - 18
Main Authors: Afonso, Suzete, da Silva, Márcia
Format: Journal Article
Language:English
Published: University of Szeged 01.01.2019
Subjects:
generalized odes
impulsive rfdes
lipschitz stability
variational lipschitz stability
ISSN:1417-3875, 1417-3875
Online Access:Get full text
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Summary: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.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2019.1.18