Ardjouni, A., Nouioua, F., Djoudi, A. (2017). Periodic Solutions for Third-Order Nonlinear Delay Differential Equations with Variable Coefficients. Khayyam Journal of Mathematics, 3(1), 12-21. doi: 10.22034/kjm.2017.44493

Abdelouaheb Ardjouni; Farid Nouioua; Ahcene Djoudi. "Periodic Solutions for Third-Order Nonlinear Delay Differential Equations with Variable Coefficients". Khayyam Journal of Mathematics, 3, 1, 2017, 12-21. doi: 10.22034/kjm.2017.44493

Ardjouni, A., Nouioua, F., Djoudi, A. (2017). 'Periodic Solutions for Third-Order Nonlinear Delay Differential Equations with Variable Coefficients', Khayyam Journal of Mathematics, 3(1), pp. 12-21. doi: 10.22034/kjm.2017.44493

Ardjouni, A., Nouioua, F., Djoudi, A. Periodic Solutions for Third-Order Nonlinear Delay Differential Equations with Variable Coefficients. Khayyam Journal of Mathematics, 2017; 3(1): 12-21. doi: 10.22034/kjm.2017.44493

Periodic Solutions for Third-Order Nonlinear Delay Differential Equations with Variable Coefficients

^{1}Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria.

^{2}Department of Mathematics, University of Annaba, P.O. Box 12, Annaba, 23000, Algeria.

Abstract

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients% \begin{align*} & x^{\prime\prime\prime}(t)+p(t)x^{\prime\prime}(t)+q(t)x^{\prime }(t)+r(t)x(t)\\ & =f\left( t,x\left( t\right) ,x(t-\tau(t))\right) +\frac{d}{dt}g\left( t,x\left( t-\tau\left( t\right) \right) \right) , \end{align*} is considered. By employing Green's function, Krasnoselskii's fixed point theorem and the contraction mapping principle, we state and prove the existence and uniqueness of periodic solutions to the third-order nonlinear delay differential equation.