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

Abstract

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