scholarly journals Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems

2020 ◽  
Vol 40 (3) ◽  
pp. 341-360
Author(s):  
Mimia Benhadri ◽  
Tomás Caraballo ◽  
Halim Zeghdoudi
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Main Tool ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Deviating Arguments ◽  
Competition System ◽  
Special Cases ◽  
Krasnoselskii Fixed Point Theorem

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.

POSITIVE PERIODIC SOLUTIONS FOR A GENERALIZED IMPULSIVE N-SPECIES GILPIN–AYALA COMPETITION SYSTEM WITH CONTINUOUSLY DISTRIBUTED DELAYS ON TIME SCALES

2011 ◽  
Vol 04 (01) ◽  
pp. 23-34 ◽  
Author(s):  
TIANWEI ZHANG ◽  
YONGKUN LI
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Competition System ◽  
Periodic Environment

In this paper, we study a generalized impulsive n-species Gilpin–Ayala competition system with continuously distributed delays on time scales in periodic environment, which is more general and more realistic than the classical Lotka–Volterra competition system. By using a fixed point theorem of strict-set-contraction, some sufficient conditions are obtained for the existence of at least one positive periodic solution. Finally, we present an example to illustrate that our results are effective.

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 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.

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 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.

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 Positive Periodic Solution of Second-Order Coupled Systems with Singularities

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Tiantian Ma
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Coupled Systems

This paper establishes the existence of periodic solution for a kind of second-order singular nonautonomous coupled systems. Our approach is based on fixed point theorem in cones. Examples are given to illustrate the main result.

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 Periodic Solutions and Nontrivial Periodic Solutions for a Class of Rayleigh-Type Equation with Two Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Meiqiang Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type Equation ◽  
Index Theorem ◽  
Rayleigh Equation ◽  
Deviating Arguments ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions

The Rayleigh equation with two deviating argumentsx′′(t)+f(x'(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=e(t)is studied. By using Leray-Schauder index theorem and Leray-Schauder fixed point theorem, we obtain some new results on the existence of periodic solutions, especially for the existence of nontrivial periodic solutions to this equation. The results are illustrated with two examples, which cannot be handled using the existing results.

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