Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47883120170101Periodic Solutions for Third-Order Nonlinear Delay Differential Equations with Variable Coefficients12214449310.22034/kjm.2017.44493ENAbdelouahebArdjouniDepartment of Mathematics and Informatics, University of Souk Ahras, P.O.
Box 1553, Souk Ahras, 41000, Algeria.FaridNouiouaDepartment of Mathematics and Informatics, University of Souk Ahras, P.O.
Box 1553, Souk Ahras, 41000, Algeria.AhceneDjoudiDepartment of Mathematics, University of Annaba, P.O. Box 12, Annaba,
23000, Algeria.Journal Article20161116In this paper, the following third-order nonlinear delay differential equation<br />with periodic coefficients%<br />begin{align*}<br />& x^{primeprimeprime}(t)+p(t)x^{primeprime}(t)+q(t)x^{prime<br />}(t)+r(t)x(t)\<br />& =fleft( t,xleft( tright) ,x(t-tau(t))right) +frac{d}{dt}gleft(<br />t,xleft( t-tauleft( tright) right) right) ,<br />end{align*}<br />is considered. By employing Green's function, Krasnoselskii's fixed point<br />theorem and the contraction mapping principle, we state and prove the<br />existence and uniqueness of periodic solutions to the third-order nonlinear<br />delay differential equation.http://www.kjm-math.org/article_44493_fca28ec0388a064bcfebffd47c16b12f.pdf