Entire solutions for a two-component competition system in a lattice

Guo, Jong‐Shenq; Wu, Chang-Hong

doi:10.2748/tmj/1270041024

Cited by 40 publications

(21 citation statements)

References 18 publications

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“…Recently, Morita and Tachibana [26] extended the existence results to the competition system (2). A discrete analogue was established by Guo and Wu [10] for the following spatially discrete competitive diffusion system…”

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confidence: 96%

Invasion entire solutions in a competition system with nonlocal dispersal

Li¹,

Zhang²,

Zhang³

2015

Discrete &Amp; Continuous Dynamical Systems - A

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This paper is concerned with invasion entire solutions of a Lotka-Volterra competition system with nonlocal dispersal, which formulate a new invasion way of the stronger species to the weaker one. We first give the asymptotic behavior of traveling wave solutions at infinity. Then by the comparison principle and sub-super solutions method, we establish the existence of invasion entire solutions which behave as two monotone waves with different speeds and coming from both sides of x-axis.2010 Mathematics Subject Classification. Primary: 35K57, 37C65; Secondary: 92D30.

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confidence: 96%

Invasion entire solutions in a competition system with nonlocal dispersal

Li¹,

Zhang²,

Zhang³

2015

Discrete &Amp; Continuous Dynamical Systems - A

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“…It is well known that the asymptotic behavior of the traveling wave solution is of great importance in investigating further properties of the traveling wave solution such as the uniqueness and stability (see, e.g., [24,25,41]), since this often determines the choice of perturbation space. On the other hand, the asymptotic behavior of traveling waves is also crucial in constructing appropriate sub-and supersolutions, which enables us to establish some other new types of entire solutions (see, e.g., [16,29,33,37]). In other words, it is very necessary and important to study the asymptotic behavior of traveling wave fronts near the limiting states.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Asymptotic behavior of traveling fronts and entire solutions for a periodic bistable competition–diffusion system

Wang

2018

Journal of Differential Equations

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This paper is concerned with a time periodic competition-diffusion systemwhere u(t, x) and v(t, x) denote the densities of two competing species, d > 0 is some constant, r i (t), a i (t) and b i (t) are T −periodic continuous functions. Under suitable conditions, it has been confirmed by Bao and Wang [J. Differential Equations 255 (2013), 2402-2435] that this system admits a periodic traveling front connecting two stable semi-trivial T −periodic solutions (p(t), 0) and (0, q(t)) associated to the corresponding kinetic system. Assume further that the wave speed is non-zero, we investigate the asymptotic behavior of the periodic bistable traveling front at infinity by a dynamical approach combined with the two-sided Laplace transform method. With these asymptotic properties, we then give some key estimates. Finally, by applying super-and subsolutions technique as well as the comparison principle, we establish the existence and various qualitative properties of entire solutions defined for all time and whole space.

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“…Recently, Morita and Tachibana [17], Guo and Wu [9], Wang and Lv [23], Wu [30] and Wu et al . [35] extended the existence of entire solutions of scalar equations to some two-component cooperative reaction-diffusion model systems.…”

Section: Introductionmentioning

confidence: 96%

Entire solutions of non-quasi-monotone delayed reaction—diffusion equations with applications

Hsu²

2014

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We are interested in finding the entire solutions of non-quasi-monotone delayed non-local reaction-diffusion equations. It is well known that the comparison principle is not applicable for such equations. To overcome this difficulty, we introduce two auxiliary quasi-monotone equations and establish some comparison arguments for the three systems. Some new types of entire solutions are then constructed using the comparison argument, the travelling wavefronts and a spatially independent solution of the auxiliary equations. We also extend our arguments to a delayed cellular neural network with non-monotonic output functions and a delayed non-local lattice differential equation with non-monotonic birth functions.

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Entire solutions for a two-component competition system in a lattice

Cited by 40 publications

References 18 publications

Invasion entire solutions in a competition system with nonlocal dispersal

Invasion entire solutions in a competition system with nonlocal dispersal

Asymptotic behavior of traveling fronts and entire solutions for a periodic bistable competition–diffusion system

Entire solutions of non-quasi-monotone delayed reaction—diffusion equations with applications

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