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

Abstract

Abstract 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 ) ) ) $(x(t)-cx(t-\delta)){''}+a(t)g(x(t))x(t)=\lambda b(t)f(t,x(t),x(t-\tau_{1}(t)),x'(t-\tau_{2}(t)))$ . By utilizing the perturbation method of positive operator and Leggett–Williams fixed point theorem, a group of sufficient conditions are established.

Keywords

• Neutral functional differential equation
• Positive periodic solution
• Delayed derivative
• Cone
• Leggett–Williams fixed point theorem