Lipschitz stability of generalized ordinary differential equations and impulsive retarded differential equations - Afonso, Suzete M. [UNESP]; da Silva, Márcia R. (University of Szeged, 2019)
We consider a class of retarded functional differential equations with preas-signed 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.
Keywords: Generalized ODEs; Impulsive RFDEs; Lipschitz stability; Variational lipschitz stability