On the Existence and Oscillatory Solutions of Multiple Delay Differential Equation

Bashar Ahmed Jawad Sharba; Aqeel Falih Jaddoa

doi:10.24996/ijs.2023.64.2.33

Authors

Bashar Ahmed Jawad Sharba Department of Mathematics, faculty of computer Science and Mathematics, University of Kufa, Najaf, Iraq
Aqeel Falih Jaddoa Department of Mathematics, College of Ibn-Al-Haitham Education for Pure Science University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-5590-7991

DOI:

https://doi.org/10.24996/ijs.2023.64.2.33

Keywords:

Existence of Nonocillatory Solutions, Oscillatory Property, Multiple Delay Differential Equation, Banach Space

Abstract

In this paper, we introduce new conditions to prove that the existence and boundedness of the solution by convergent sequences and convergent series. The theorem of Krasnoselskii, Lebesgue’s dominated convergence theorem and fixed point theorem are used to get some sufficient conditions for the existence of solutions. Furthermore, we get sufficient conditions to guarantee the oscillatory property for all solutions in this class of equations. An illustrative example is included as an application to the main results.