scholarly journals Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Zhenguo Luo ◽  
Liping Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Volterra System

By using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays:xi′(t)=xi(t)[ri(t)-∑j=1naij(t)xj(t)-∑j=1n‍bij(t)∫-τij0‍fij(ξ)xj(t+ξ)dξ-∑j=1n‍cij(t)∫-σij0‍gij(ξ)xj′(t+ξ)dξ],  Δxi(tk)=-Iik(xi(tk)),  i=1,2,…,n,  k=1,2,….Some verifiable criteria are established easily.

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 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 PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

scholarly journals Existence of Positive Periodic Solutions for a Class of Higher-Dimension Functional Differential Equations with Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhang Suping ◽  
Jiang Wei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Higher Dimension ◽  
Positive Periodic Solutions ◽  
Krasnoselskii Fixed Point Theorem ◽  
Functional Differential

By employing the Krasnoselskii fixed point theorem, we establish some criteria for the existence of positive periodic solutions of a class ofn-dimension periodic functional differential equations with impulses, which improve the results of the literature.

Three Positive Periodic Solutions of Nonlinear Functional Differential Equations with Impulse Effects

2011 ◽  
Vol 403-408 ◽  
pp. 1319-1321
Author(s):  
Lei Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Nonlinear Functional ◽  
Functional Differential

In this paper, a type of nonlinear functional differential equations with impulse effects are studied by using the Leggett-Williams fixed point theorem.

scholarly journals EXISTENCE AND EXPONENTIAL STABILITY OF POSITIVE PERIODIC SOLUTIONS FOR SECOND-ORDER DYNAMIC EQUATIONS

2020 ◽  
Vol 6 (1) ◽  
pp. 42
Author(s):  
Faycal Bouchelaghem ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Second Order ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Main Method

In this article, we establish the existence of positive periodic solutions for second-order dynamic equations on time scales. The main method used here is the Schauder fixed point theorem. The exponential stability of positive periodic solutions is also studied. The results obtained here extend some results in the literature. An example is also given to illustrate this work.

scholarly journals Positive periodic solutions for second order impulsive differential equations

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Jianhua Shen ◽  
Weibing Wang ◽  
Zhimin He
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Continuous Equation

AbstractThe existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using fixed point theorem in cone, new existence results of positive periodic solutions are obtained without assuming the existence of positive periodic solutions of the corresponding continuous equation.

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 Existence of Periodic Positive Solutions for Abstract Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Shugui Kang ◽  
Yaqiong Cui ◽  
Jianmin Guo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Positive Periodic Solutions

We will consider the existence of multiple positive periodic solutions for a class of abstract difference equations by using the well-known fixed point theorem (due to Krasnoselskii).

scholarly journals Multiple Positive Periodic Solutions for Functional Differential Equations with Impulses and a Parameter

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Zhenguo Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Krasnoselskii Fixed Point Theorem ◽  
Functional Differential

We apply the Krasnoselskii fixed-point theorem to investigate the existence of multiple positive periodic solutions for a class of impulsive functional differential equations with a parameter; some verifiable sufficient results are established easily. In particular, our results extend and improve some previous results.

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