Existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable delay

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdelouaheb Ardjouni ◽  
Ali Rezaiguia ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Main Tool ◽  
The Other ◽  
Variable Delay ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Completely Continuous ◽  
Neutral Differential Equations

Abstract.In this article we study the existence of positive periodic solutions for a fourth-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnoselskii's fixed point theorem dealing with a sum of two mappings, one is a contraction and the other one is completely continuous.

scholarly journals Periodicity and positivity in nonlinear neutral integro-dynamic equations with variable delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 117-132
Author(s):  
Malik Belaid ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Dynamic Equations ◽  
Variable Delay ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Completely Continuous ◽  
Continuous Map ◽  
Uniqueness Results

Let T be a periodic time scale. We use Krasnoselskii's fixed point theorem for a sum of two operators to show new results on the existence of periodic and positive periodic solutions of a nonlinear neutral integro-dynamic equation with variable delay. We invert this equation to construct a sum of a contraction and a completely continuous map which is suitable for applying Krasnoselskii's theorem. The uniqueness results of this equation are studied by the contraction mapping principle.

Positive periodic solutions for singular fourth-order differential equations with a deviating argument

2018 ◽  
Vol 148 (3) ◽  
pp. 605-617 ◽  
Author(s):  
Fanchao Kong ◽  
Zaitao Liang
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Deviating Argument ◽  
Small Force ◽  
Image Position ◽  
Fourth Order Differential Equation

In this paper, we study the singular fourth-order differential equation with a deviating argument:By using Mawhin's continuation theorem and some analytic techniques, we establish some criteria to guarantee the existence of positive periodic solutions. The significance of this paper is that g has a strong singularity at x = 0 and satisfies a small force condition at x = ∞, which is different from the known ones in the literature.

scholarly journals Positive periodic solutions for second-order neutral differential equations with time-dependent deviating arguments

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3627-3638 ◽  
Author(s):  
Zhibo Cheng ◽  
Feifan Li ◽  
Shaowen Yao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Time Dependent ◽  
Positive Periodic Solutions ◽  
Deviating Arguments ◽  
Neutral Differential Equations

In this paper, we consider a kind of second-order neutral differential equation with timedependent deviating arguments. By applications of Krasnoselskii?s fixed point theorem, sufficient conditions for the existence of positive periodic solutions are established.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

scholarly journals Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

2018 ◽  
Vol 36 (2) ◽  
pp. 185
Author(s):  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scale ◽  
Variable Coefficients ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations ◽  
Compact Map

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

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