Periodic Solutions of a Second Order Nonlinear Differential Equations with Delay and Variable Coefficients in Extend b-metric Space

In this paper, we obtain some criteria for the existence of the periodic solution for the second order nonlinear functional differential equations with delay and variable coefficients
$x^{\prime\prime}(t)+p(t)x^{\prime}(t)+q(t)x(t)=\lambda h(t)f(t, x(t-\tau(t))+r(t)x^{\prime}(t)$
, by means of fixed point theorem in extend b-metric space.