Existence and Qualitative Property of Differential Equation with Delayed Arguments

Aqeel Falih Jaddoa; Bashar Ahmed Jawad Sharba

doi:10.24996/ijs.2023.64.9.30

Authors

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
Bashar Ahmed Jawad Sharba Department of Mathematics, faculty of computer Science and Mathematics, University of Kufa, Najaf,

DOI:

https://doi.org/10.24996/ijs.2023.64.9.30

Keywords:

Existence of Nonocillatory Bounded Solutions, Oscillation Criteria, Second Order Multiple Delay Differential Equation, Banach Space

Abstract

In this paper, some conditions to guarantee the existence of bounded solution to the second order multi delayed arguments differential equation are given. The Krasnoselskii theorem used to the Lebesgue’s dominated convergence and fixed point to obtain some new sufficient conditions for existence of solutions. Some important lemmas are established that are useful to prove the main results for oscillatory property. We also submitted some sufficient conditions to ensure the oscillation criteria of bounded solutions to the same equation.