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)-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.
Highlights
1 Introduction In the present work, we study the existence of three positive periodic solutions for the second order neutral functional differential equation of the form x(t) – cx(t – δ) + a(t)g x(t) x(t) = λb(t)f t, x(t), x t – τ1(t), x t – τ2(t), (1)
Neutral functional differential equations have a wide range of applications in the field of physics, biology, economics, and so on, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14] for more details
It is important to study the periodic solutions of such models
Summary
Li [14] discussed the existence and nonexistence of positive ω-periodic solutions of second order neutral functional differential equations with delayed derivative in nonlinear term by using the positive operator perturbation method and the fixed point index theory x(t) – cx(t – δ) + a(t)x(t) = f t, x(t), x t – τ (t) , x t – γ (t) , where δ > 0, |c| < 1, a ∈ C(R, ∞) is an ω periodic function, f : R × [0, ∞)2 × R → [0, ∞) is continuous, and f (t, u, v, w) is ω-periodic with respect to t, τ , γ ∈ C(R, [0, ∞)) are ωperiodic functions.
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