Existence and Uniqueness of a Periodic Solution to a Certain Third-Order Neutral Functional Differential Equation

Rasha Osman Ahmed Taie, Mona Ghaleb Abdullah Alwaleedy


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.


Periodic solution, coincidence degree theory, generalized neutral operator, neutral differential equation.

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ISSN: 1331-0623 (Print), 1848-8013 (Online)