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 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 of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

scholarly journals Existence of triple positive periodic solutions of a functional differential equation depending on a parameter

2004 ◽  
Vol 2004 (10) ◽  
pp. 897-905 ◽  
Author(s):  
Xi-lan Liu ◽  
Guang Zhang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Functional Differential

We establish the existence of three positive periodic solutions for a class of delay functional differential equations depending on a parameter by the Leggett-Williams fixed point theorem.

scholarly journals On the Existence and Stability of Periodic Solutions for a Nonlinear Neutral Functional Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yueding Yuan ◽  
Zhiming Guo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Neutral Functional Differential Equation ◽  
Existence And Stability ◽  
Functional Differential

This paper deals with the existence and stability of periodic solutions for the following nonlinear neutral functional differential equation(d/dt)Dut=p(t)-au(t)-aqu(t-r)-h(u(t),u(t-r)).By using Schauder-fixed-point theorem and Krasnoselskii-fixed-point theorem, some sufficient conditions are obtained for the existence of asymptotic periodic solutions. Main results in this paper extend the related results due to Ding (2010) and Lopes (1976).

scholarly journals Multiplicity Results for Variable-Coefficient Singular Third-Order Differential Equation with a Parameter

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhibo Cheng ◽  
Yun Xin
Keyword(s):  
Differential Equation ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Positive Periodic Solutions ◽  
Third Order ◽  
Multiplicity Results ◽  
Third Order Differential Equation ◽  
Krasnoselskii Fixed Point Theorem

We investigate a class of variable coefficients singular third-order differential equation with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. By applications of Green’s function and the Krasnoselskii fixed point theorem, sufficient conditions for the existence of positive periodic solutions are established.

scholarly journals On Positive Periodic Solutions to Nonlinear Fifth-Order Differential Equations with Six Parameters

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Yunhai Wang ◽  
Fanglei Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Function ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Existence And Multiplicity ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fifth Order

We study the existence and multiplicity of positive periodic solutions to the nonlinear differential equation:u5(t)+ku4(t)-βu3-ξu″(t)+αu'(t)+ωu(t)=λh(t)f(u),  in  0≤t≤1,  ui(0)=ui(1),  i=0,1,2,3,4, wherek,α,ω,λ>0,  β,ξ∈R,h∈C(R,R)is a 1-periodic function. The proof is based on the Krasnoselskii fixed point theorem.

scholarly journals Existence of Mild solutions of Fractional order Hybrid Deferential Equations with Impulses

2019 ◽  
pp. 718-725
Author(s):  
Prakash Kumar H. Patel
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Fractional Order Differential Equation ◽  
Hybrid Fixed Point Theorem

This article derive sufficient conditions for existence of mild solution for the hybrid fractional order differential equation with impulses of the form eq1 on a Banach space X over interval [0,T]. The results are obtained using the concept of hybrid fixed point theorem. Finally an illustration is added to show validation of the derived results.

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

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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