On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

Abstract

We prove that the totally nonlinear second-order neutral diferential equation dt2x(t) + p(t)ddtx(t) + q(t)h(x(t)) =ddtc(t, x(t − τ (t))) + f(t, ρ(x(t)), g(x(t − τ (t)))) has positive periodic solutions by employing the Krasnoselskii-Burton hybrid fixed point