Existence of Solutions for Nonlinear Impulsive Multiple Retarded Differential and Impulsive Integro-Differential Equations of Second Order

Abstract

. In this paper, we deal with the existence of solutions of certain impulsive multiple retarded differential equations (ImMRDEs) and impulsive multiple retarded integro-differential equations (ImMRIDEs) of second order. We prove two new results on the existence of solutions of the considered ImMRDE and ImMRIDE of second order. The technique of the proofs depends on the Schaefer fixed point theorem (Schaefer FPT) and fixed moments of impulse effects. The outcomes of this paper have more general forms and improve the known results in the relevant literature, and they have new contributions to the theory of impulsive retarded differential equations (ImMRDEs). The outcomes of this paper have also new complementary properties for the works in relation to the symmetry of impulsive differential equations (ImDEs) of second order with or without delay, impulsive retarded integro-differential equations (ImMRIDEs) of second order, and some others.