关键词: 先验估计, 非常数正解的存在性, 避难所, 扩散

Abstract:

The steadystates of a diffusive preypredator system incorporating a prey refuge subject to homogeneous Neumann boundary condition were considered, and some

improved results of the positive steady states solutions were derived. A priori estimates for positive solutions were established, and the nonexistence of nonconstant

positive steady states was given by using the energy method. The existence of nonconstant positive steady states was obtained by using the topological degree theory.

Key words: prey refuge, diffusion, priori estimate, nonconstant positive solution existence