scholarly journals Speed determinacy of the traveling waves for a three species time-periodic Lotka-Volterra competition system

2021 ◽  
Author(s):  
Qiong Wu ◽  
Chaohong Pan ◽  
Hongyong Wang
Keyword(s):  
Traveling Waves ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Lower Solution ◽  
Competition System ◽  
Periodic Traveling Waves ◽  
Minimal Wave Speed ◽  
Speed Selection ◽  
Time Periodic ◽  
Selection Of

In this paper, speed selection of the time periodic traveling waves for a three species time-periodic Lotka-Volterra competition system is studied via the upper-lower solution method as well as the comparison principle. Through constructing specific types of upper and lower solutions to the system, the speed selection of the minimal wave speed can be determined under some sets of sufficient conditions composed of the parameters in the system.

TRAVELING WAVES FOR A SIRS MODEL WITH NONLOCAL DIFFUSION

2012 ◽  
Vol 05 (05) ◽  
pp. 1250036 ◽  
Author(s):  
XIAOJING YU ◽  
CHUFEN WU ◽  
PEIXUAN WENG
Keyword(s):  
Traveling Waves ◽  
Sufficient Conditions ◽  
Traveling Wave Solutions ◽  
Iteration Scheme ◽  
Lower Solution ◽  
Nonlocal Diffusion ◽  
Well Posedness ◽  
Upper Solution ◽  
Sirs Model ◽  
Two Equilibria

In this paper, we study a delayed SIRS model with nonlocal diffusion. The well posedness of the model is investigated. Furthermore, we concern with the problem of traveling wave solutions. By using the partial quasi-monotone condition, cross-iteration scheme and fixed-point theorem, sufficient conditions are derived for the existence of traveling waves connecting the two equilibria which depends on the existence of a pair of upper solution and lower solution. We in fact construct a pair of upper solution and lower solution concretely to guarantee the existence of traveling waves.

Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations

2009 ◽  
Vol 16 (4) ◽  
pp. 617-628
Author(s):  
Guoping Chen ◽  
Jianhua Shen
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Lower Solution ◽  
Point Boundary ◽  
Functional Differential ◽  
Extreme Solutions

Abstract This paper is concerned with the existence of extreme solutions of nonlinear three-point boundary value problems for a class of first order impulsive functional differential equations. In the presence of a lower solution α and an upper solution β with the classical condition α ≤ β or the reversed ordering condition β ≤ α, some sufficient conditions for the existence of extreme solutions are obtained by using the method of upper and lower solutions coupled with the monotone iterative technique.

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