Logistic type equations on R~N by a squeezing method involving boundary blow-up solutions

摘要

We study, on the entire space R~N (N ≥ 1), the diffusive logistic equation u_t - Δu = λu - 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 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].