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Zbl 0778.34006
Zinner, B.; Harris, G.; Hudson, W.
Traveling wavefronts for the discrete Fisher's equation. (English)
[J] J. Differ. Equations 105, No.1, 46-62 (1993). ISSN 0022-0396

Summary: Using continuation and comparison methods we obtain conditions for the existence and nonexistence of traveling wavefronts with speed $c$ of the discrete Fisher's equation $$\dot u\sb n=d(u\sb{n-1}-2u\sb n+u\sb{n+1})+f(u\sb n),\qquad n\in\bbfZ,$$ where $d$ is a positive number and $f$ denotes a Lipschitz continuous function satisfying $f(0)=f(1)=0$ and $f(x)>0$ for $0<x<1$. The results are sharp if $f$ is differentiable at 0 and satisfies $f'(0)x\ge f(x)$ for $x>0$.

MSC 2000:: *34A35 ODE of infinite order

Keywords: continuation; comparison methods; existence; nonexistence; traveling wavefronts; discrete Fisher's equation

Cited in: Zbl 1092.34012

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