New results on periodic solutions for a nonlinear fourth-order iterative differential equation

Rabah Khemis\(^{a,*}\), Ahl`eme Bouakkaz\(^a\)

\(^a\) Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955 Skikda,Algeria

Correspondence should be addressed to: kbra28@yahoo.fr

Copyright © 2022 Rabah Khemis, Ahl`eme Bouakkaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 10 November 2021; Accepted: 07 October 2022; Published Online: 14 October 2022.

Abstract

The key task of this paper is to investigate a nonlinear fourth-order delay differential equation. By virtue of the fixed point theory and the Green’s functions method, we establish some new results on the existence, uniqueness and continuous dependence on parameters of periodic solutions. In addition, an example is given to corroborate the validity of our main results. Up to now, no work has been carried out on this topic. So, the findings of this paper are new and complement the available works in the literature to some degree.

Keywords:

Periodic solutions, Iterative differential equations, fixed point theorems, Green’s function.