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

• Main Authors: Suzete Afonso, Márcia da Silva
• Format: Article
• Language: English
• Published: University of Szeged 2019-03-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: generalized odes; impulsive rfdes; variational lipschitz stability; lipschitz stability
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=7216

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.