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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

Puni tekst: engleski pdf 409 Kb

str. 257-276

preuzimanja: 108



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.

Ključne riječi

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

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