Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Journal of Dynamical and Control Systems

19-04-2020

Front-like Entire Solutions for a Lotka-Volterra Weak Competition System with Nonlocal Dispersal

Published in: Journal of Dynamical and Control Systems | Issue 1/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper is concerned with the front-like entire solutions for a Lotka-Volterra weak competition system with nonlocal dispersal. Here, an entire solution means a classical solution defined for all space and time variables. This system has traveling wavefronts and enjoys the comparison principle. Based on these traveling wavefronts, we construct some super- and sub-solutions. Then, by using the comparison principle and the super- and sub-solutions method, we establish the existence of front-like entire solutions which behave as two wavefronts coming from the both sides of x-axis. Moreover, some properties of the front-like entire solutions are obtained.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Bao X-X, Li W-T, Wang Z-C. Uniqueness and stability of time-periodic pyramidal fronts for a periodic competition-diffusion system. Commun Pure Appl Anal 2020;19:253–277.MathSciNetCrossRef
2.
Chen X, Guo JS. Existence and uniqueness of entire solutions for a reaction-diffusion equation. J Differential Equations 2005;212:62–84.MathSciNetCrossRef
3.
Chen X, Guo JS, Ninomiya H. Entire solutions of reaction-diffusion equations with balanced bistable nonlinearity. Proc Roy Soc Edinburgh Sect A 2006;136:1207–1237.MathSciNetCrossRef
4.
Fang J, Zhao X-Q. Traveling waves for monotone semiflows with weak compactness. SIAM J Math Anal 2014;46:3678–3704.MathSciNetCrossRef
5.
6.
Guo JS, Morita Y. Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations. Discrete Contin Dyn Syst 2005;12:193–212.MathSciNetCrossRef
7.
Guo JS, Wu CH. Entire solutions for a two-component competition system in a lattice. Tohoku Math J 2010;62:17–28.MathSciNetCrossRef
8.
9.
Hamel F, Nadirashvili N. Travelling fronts and entire solutions of the Fisher-KPP equation in RN. Arch Rational Mech Anal 2001;157:91–163.MathSciNetCrossRef
10.
Hou X, Wang B, Zhang ZC. The mutual inclusion in a nonlocal competitive Lotka Volterra system. Japan J Indust Appl Math 2014;31:87–110.MathSciNetCrossRef
11.
Li K, Huang JH, Li X. Asymptotic behavior and uniqueness of traveling wave solutions in a delayed nonlocal dispersal competitive system. Commun Pure Appl Anal 2017;16:131–150.MathSciNetCrossRef
12.
Li W-T, Sun Y-J, Wang Z-C. Entire solutions in the Fisher-KPP equation with nonlocal dispersal. Nonlinear Anal Real World Appl 2010;11:2302–2313.MathSciNetCrossRef
13.
Li W-T, Wang Z-C, Wu J. Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity. J Differential Equations 2008;245:102–129.MathSciNetCrossRef
14.
Li W-T, Zhang L, Zhang G-B. Invasion entire solutions in a competition system with nonlocal dispersal. Discrete Contin Dyn Syst 2015;35:1531–1560.MathSciNetCrossRef
15.
Morita Y, Ninomiya H. Entire solutions with merging fronts to reaction-diffusion equations. J Dynam Differential Equations 2006;18:841–861.MathSciNetCrossRef
16.
Morita Y, Tachibana K. An entire solution to the Lotka-Volterra competition-diffusion equations. SIAM J Math Anal 2009;40:2217–2240.MathSciNetCrossRef
17.
Pan S, Lin G. Invasion traveling wave solutions of a competitive system with dispersal. Bound Value Probl 2012;120:1–11.MathSciNetMATH
18.
Sun Y-J, Li W-T, Wang Z-C. Entire solutions in nonlocal dispersal equations with bistable nonlinearity. J Differential Equations 2011;251:551–581.MathSciNetCrossRef
19.
Wang MX, Lv G. Entire solutions of a diffusion and competitive Lotka-Volterra type system with nonlocal delayed. Nonlinearity 2010;23:1609–1630.MathSciNetCrossRef
20.
Wang XH, Lv G. Entire solutions for Lotka-Volterra competition-diffusion model. Int J Biomath 2013;6:1350020. (13 pages).MathSciNetCrossRef
21.
Wang Y, Li X. Some entire solutions to the competitive reaction diffusion system. J Math Anal Appl 2015;430:993–1008.MathSciNetCrossRef
22.
Wang Y, Li X. Entire solutions for the classical competitive Lotka-Volterra system with diffusion in the weak competition case. Nonlinear Anal RWA 2018;42:1–23.MathSciNetCrossRef
23.
Wang Y, Liu GR, Li X. Entire solutions in a delayed nonlocal dispersal competitive system. Int J Bioma 2019;12:1950035.MathSciNetCrossRef
24.
Weng P, Zhao X -Q. Spreading speed and traveling waves for a multi-type SIS epidemic model. J Differential Equations 2006;229:270–296.MathSciNetCrossRef
25.
Wu S-L, Wang H. Front-like entire solutions for monostable reaction-diffusion systems. J Dynam Differential Equations 2013;25:505–533.MathSciNetCrossRef
26.
Wu S-L, Sun Y-J, Liu S. Traveling fonts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity. Discrete Contin Dyn Syst 2013;33:921–946.MathSciNetCrossRef
27.
Wu S-L, Ruan S. Entire solutions for nonlocal dispersal equations with spatio-temporal delay: monostable case. J Differential Equations 2015;258:2435–2470.MathSciNetCrossRef
28.
Yagisita H. Back and global solutions characterizing annihilation dynamics of traveling fronts. Publ Res Inst Math Sci 2003;39:117–164.MathSciNetCrossRef
29.
Yu Z-X, Yuan R. Existence of traveling wave solutions in nonlocal reaction-diffusion systems with delays and applications. ANZIAM J 2009;51:49–66.MathSciNetCrossRef
30.
Yu Z-X, Xu F, Zhang W-G. Stability of invasion traveling waves for a competition system with nonlocal dispersals. Appl Anal 2017;96:1107–1125.MathSciNetCrossRef
31.
Zhang G-B. Non-monotone traveling waves and entire solutions for a delayed nonlocal dispersal equation. Appl Anal 2017;96:1830–1866.MathSciNetCrossRef
32.
Zhang G-B, Ma R. Front-like entire solutions for delayed nonlocal dispersal equation with convolution type bistable nonlinearity. Rocky Mountain J Math 2017;47: 1355–1404.MathSciNetCrossRef
33.
Zhang G-B, Ma R, Li X-S. Traveling waves for a Lotka-Volterra strong competition system with nonlocal dispersal. Discrete Contin Dyn Syst Ser B 2018;23: 587–608.MathSciNetMATH
34.
Zhang L, Li B. Traveling wave solutions in an integro-differential competition model. Discrete Contin Dyn Syst Ser B 2012;17:417–428.MathSciNetCrossRef
Metadata
Title
Front-like Entire Solutions for a Lotka-Volterra Weak Competition System with Nonlocal Dispersal
Publication date
19-04-2020
Published in
Journal of Dynamical and Control Systems / Issue 1/2021
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-020-09487-1

Premium Partners

    Image Credits