Three positive periodic solutions of second order nonlinear neutral functional differential equations with delayed derivative.

This paper deals with the existence of three positive periodic solutions for a class of second order neutral functional differential equations involving the delayed derivative term in nonlinearity (x (t) − c x (t − δ)) ″ + a (t) g (x (t)) x (t) = λ b (t) f (t , x (t) , x (t − τ 1 (t)) , x ′ (t − τ 2 (t))) . By utilizing the perturbation method of positive operator and Leggett–Williams fixed point theorem, a group of sufficient conditions are established. [ABSTRACT FROM AUTHOR]