scholarly journals On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiang Li ◽  
Yongxiang Li
Keyword(s):  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Index Theory ◽  
Second Order ◽  
Multiple Delays ◽  
First Eigenvalue ◽  
Fixed Point Index Theory ◽  
Existence Conditions ◽  
Functional Differential ◽  
Periodic Boundary Problem

The existence results of positiveω-periodic solutions are obtained for the second-order functional differential equation with multiple delaysu″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), wherea(t)∈C(ℝ)is a positiveω-periodic function,f:ℝ×[0,+∞)n+1→[0,+∞)is a continuous function which isω-periodic int, andτ1(t),…,τn(t)∈C(ℝ,[0,+∞))areω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

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.

On positive periodic solutions of linear second order functional differential equations

2017 ◽  
Vol 24 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Eugene I. Bravyi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Positive Periodic Solutions ◽  
Functional Differential

AbstractThe periodic boundary value problem for linear second order functional differential equations is considered. Sharp sufficient conditions for the positiveness of solutions are obtained.

scholarly journals Multiple Periodic Solutions for a Class of Second-Order Neutral Impulsive Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Jingli Xie ◽  
Zhiguo Luo ◽  
Yuhua Zeng
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Functional Differential Equations ◽  
Point Theory ◽  
Second Order ◽  
Multiple Periodic Solutions ◽  
Functional Differential

In this paper, we study a class of second-order neutral impulsive functional differential equations. Under certain conditions, we establish the existence of multiple periodic solutions by means of critical point theory and variational methods. We propose an example to illustrate the applicability of our result.

scholarly journals Positive Periodic Solutions of Second-Order Differential Equations with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yongxiang Li
Keyword(s):  
Periodic Solutions ◽  
Fixed Point Index ◽  
Order Differential Equation ◽  
Index Theory ◽  
Existence Results ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Point Index ◽  
Second Order Differential Equations ◽  
Fixed Point Index Theory

The existence results of positiveω-periodic solutions are obtained for the second-order differential equation with delays−u″+a(t)=f(t,u(t−τ1),...,u(t−τn)), wherea∈C(ℝ,(0,∞))is aω-periodic function,f:ℝ×[0,∞)n→[0,∞)is a continuous function, which isω-periodic int, andτ1,τ2,...,τnare positive constants. Our discussion is based on the fixed point index theory in cones.

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