Existence of positive stationary solutions for a diffusive variable-territory predator-prey model

摘要

We consider the steady-state diffusive variable-territory predator-prey system where α(x) is a non-negative continuous function on, vanishing on a sub-domain is a constant, and is a parameter. We prove that there exists a such that the system has at least one positive solution (u, v) for each, and it has no positive solution for any, where is the first eigenvalue of-Δ on Ω0 with homogeneous Dirichlet boundary condition.