Existence and Uniqueness of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equations with Constant Delays

2006 ◽  
Vol 22 (2) ◽  
pp. 287-296
Author(s):  
Bing-wen Liu ◽  
Li-hong Huang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

Existence of positive periodic solutions for a class of second-order neutral functional differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
He Yang ◽  
Lu Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fixed Point Index ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Index Theory ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Fixed Point Index Theory ◽  
Functional Differential

Abstract In this paper, under some ordered conditions, we investigate the existence of positive ω-periodic solutions for a class of second-order neutral functional differential equations with delayed derivative in nonlinearity of the form (x(t) − cx(t − δ))″ + a(t)g(x(t))x(t) = λb(t)f(t, x(t), x(t − τ 1(t)), x′(t − τ 2(t))). By utilizing the perturbation method of a positive operator and the fixed point index theory in cones, some sufficient conditions are established for the existence as well as the non-existence of positive ω-periodic solutions.

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