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Journal of the London Mathematical Society 2001 64(1):107-124; doi:10.1017/S0024610701002289
© 2001 by London Mathematical Society
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© The London Mathematical Society

Logistic Type Equations on RN by a Squeezing Method Involving Boundary Blow-Up Solutions

Yihong Du and Li Ma

School of Mathematical and Computer Sciences, University of New England Armidale, NSW 2351, Australia, ydu{at}turing.une.edu.au
Department of Applied Mathematics, Tsinghua University Beijing, China, lma{at}math.tsinghua.edu.cn

Received 12 May 2000. Revision received 9 October 2000.

We study, on the entire space RN(N ≥ 1), the diffusive logistic equation

ut–{Delta}u={lambda}u–up, u≥0 (1.1)

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 {lambda} = 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].


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