Original scientific paper
Existence and uniqueness of a periodic solution to a certain third-order neutral functional differential equation
Rasha Osman Ahmed Taie
; Department of Mathematics, Faculty of Science, Assiut University, Assiut , Egypt
Mona Ghaleb Abdullah Alwaleedy
; Department of Mathematics, Taiz University, Taiz, Yemen
Abstract
In this paper, by applying Mawhin's continuation theorem of the coincidence degree theory, some sufficient conditions for the existence and uniqueness of an \(\omega\)-periodic solution for the following third-order neutral functional differential equation are established
\(\dfrac{d^{3}}{dt^{3}}\bigg ( x(t)-d(t)x\big (t-\delta(t)\big ) \bigg )+a(t)\ddot{x}(t)+b(t)f\big (t,\dot{x}(t)\big )+\sum_{i=1}^{n}c_{i}(t)g\big (t,x(t-\tau_{i}(t))\big )=e(t)\).
Moreover, we present an example and a graph to demonstrate the validity of analytical conclusion.
Keywords
Hrčak ID:
285136
URI
Publication date:
13.11.2022.
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