Existence of periodic solutions for generalized nonlinear third-order delay differential equations

Abstract

In this manuscript, we investigate the existence of solution to generalized third-order non-linear delay differential equation with periodic coefficients, which includes many important integral and functional equations that arise in nonlinear analysis and its applications. Our results are obtained by implementing Schauder’s fixed point fixed point theorem and rely on a generalization of Ascoli-Arzel´a theorem. Moreover, an example is offered to define the primary results.