Positive solutions of a diffusive predator-prey model with modified Leslie-Gower and Holling-type II schemes

摘要

In this paper, we investigate the existence, multiplicity and stability of positive solutions to a prey-predator model with modified Leslie-Gower and Holling-type II schemes {-Δu = u (a _1 -bu - c _1 v/u +k _1) in Ω -Δv = v(a _2 - c _2 v/u +k _2 in Ω, u ≥0, v≥0 in Ω, u=v=0, on ?Ω, where Ω?R{double-struck} ~N (N≥1) is a bounded domain with a smooth boundary ?Ω, the parameters a _i, b, c _i, k _i (i=1, 2) are positive numbers, u and v are the respective populations of prey and predator. Here, we say (u,v) with u|?Ω=v|?Ω=0 is a positive solution of problem (P) if (u,v) is a solution of (P) and u,v>0 in Ω.