On the Existence of Results for Multiple Retarded Differential and Integro-Differential Equations of Second Order

Abstract

. In this research paper, we bear in mind a class of nonlinear impulsive delay differential equations (IDDEs) and impulsive delay integro-differential equations (IDIDEs) of second order with multiple constant delays. We depict sufficient hypotheses for the existence of solutions (EOS) of these IDDEs and IDIDEs of second order. Based upon the Schaefer fixed point theorem (Schaefer FPT) and control by impulses, we gain the proofs in relation to the EOS of the IDDEs and the IDIDEs of second order. The effects of impulses are emphasized in the content of the proofs. The outcomes of this research paper have more general forms and make new improvements in relation to the some recent ones of the literature.