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

Abstract

In this paper, the following third-order nonlinear delay differential equationwith periodic coefficients%begin{align*}& x^{primeprimeprime}(t)+p(t)x^{primeprime}(t)+q(t)x^{prime}(t)+r(t)x(t)\& =fleft( t,xleft( tright) ,x(t-tau(t))right) +frac{d}{dt}gleft(t,xleft( t-tauleft( tright) right) right) ,end{align*}is considered. By employing Green's function, Krasnoselskii's fixed pointtheorem and the contraction mapping principle, we state and prove theexistence and uniqueness of periodic solutions to the third-order nonlineardelay differential equation.