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LOGISTIC TYPE EQUATIONS ON ℝN BY A SQUEEZING METHOD INVOLVING BOUNDARY BLOW-UP SOLUTIONS

Published online by Cambridge University Press:  24 August 2001

YIHONG DU  and
LI MA
YIHONG DU
Affiliation:
School of Mathematical and Computer Sciences, University of New England, Armidale, NSW 2351, Australia; ydu@turing.une.edu.au
LI MA
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing, China; lma@math.tsinghua.edu.cn
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Abstract

We study, on the entire space ℝN(N [ges ] 1), the diffusive logistic equation

and its generalizations. Here p > 1 is a constant. Problem (1.1) plays an important role in understanding various population models and some other problems in applied mathematics. When λ = 1 and p = 2, it is also known as the Fisher equation and KPP equation, due to the pioneering works of Fisher [8] and Kolmogoroff, Petrovsky and Piscounoff [18].

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 107 - 124
Copyright
The London Mathematical Society 2001

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