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.

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.

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 EXISTENCE OF SOLUTIONS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

1999 ◽  
Vol 30 (4) ◽  
pp. 299-309
Author(s):  
K. BALACHANDRAN ◽  
S. MARSHAL ANTHONI
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Cosine Families ◽  
Functional Differential

Sufficient conditions for existence of mild solutions for second order neutral functional differential equations are established by using the theory of strongly continuous cosine families and the Schaefer theorem.

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