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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)) ) + d dt g ( 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 nonlinear delay differential equation.

Existence of positive periodic solutions for third-order nonlinear delay differential equations with variable coefficients