Periodic behaviour of solution for a kind of third-order neutral delay differential equation

Articles in Press

Document Type : Original papers

Authors

1 Department of Mathematics, Faculty of Science, New Valley University

2 Department of Mathematics, Faculty of Science, New Valley University, Egypt, El-Khargah.

Abstract

In the present paper, we establish sufficient conditions for the existence and
uniqueness of T−periodic solution for a kind of the third-order neutral delay differential equation as the following
(x(t) − αx(t − σ))''' + φ(t, x'
(t))x
''(t) + ψ1(x(t − r(t)))x'
(t)
+ ψ2(t, x(t − r(t))) =
p(t),
where T > 0, T−periodic in their first argument , α and σ are constants with |α| < 1. Here, we introduce sufficient conditions for the
existence and uniqueness of periodic solution.
Our approach is based on the continuation theorem of Mawhin’s
coincidence degree theory and analysis technique. The results
obtained in this investigation extend many existing and exciting
results on nonlinear third-order delay differential equation. Our results improve
and form a complement to some results that can be found in the literature.

An example is given to illustrate the the importance of the topic and the main results obtained.

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New Valley University Journal of Basic and Applied Sciences

Articles in Press, Accepted Manuscript
Available Online from 29 May 2022

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