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

Authors:	Du Yihong; Ma Li

Institution:	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

Abstract:	We study, on the entire space R^N(N $≥$ 1), the diffusive logisticequation u_t– ${Delta}$ u= ${lambda}$ u–u^p, u $≥$ 0 (1.1) and its generalizations. Here p > 1 is a constant. Problem(1.1) plays an important role in understanding various populationmodels and some other problems in applied mathematics. When ${lambda}$ = 1 and p = 2, it is also known as the Fisher equation andKPP equation, due to the pioneering works of Fisher 8] andKolmogoroff, Petrovsky and Piscounoff 18].

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