##### Title: Existence of Positive Periodic Solutions for a Third-Order Delay Differential Equation

##### Pages: 136-143

##### Cite as:

Farid Nouioua, Abdelouaheb Ardjouni, Abdelkerim Merzougui, Ahcene Djoudi, Existence of Positive Periodic Solutions for a Third-Order Delay Differential Equation, Int. J. Anal. Appl., 13 (2) (2017), 136-143.#### Abstract

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients

x′′′(t)+p(t)x′′(t)+q(t)x′(t)+r(t)x(t)=f(t,x(t),x(t-τ(t)))+c(t)x′(t-τ(t)),

is considered. By employing Green's function and Krasnoselskii's fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.

x′′′(t)+p(t)x′′(t)+q(t)x′(t)+r(t)x(t)=f(t,x(t),x(t-τ(t)))+c(t)x′(t-τ(t)),

is considered. By employing Green's function and Krasnoselskii's fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.

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