Abstract:

A kind of predator-prey model between two species incorporating a constant prey refuge is investigated. The stability of the positive constant solution of steady state system is discussed making use of eigenvalue theory. A priori-estimate of the positive solutions is given based on the maximum principle and Harnack inequality. Finally, by means of the energy method and topological degree theory,the non-existence of non-constant positive steady states is given and the existence of non-constant positive steady states is obtained,respectively.

Key words:  prey refuge; priori estimate; non-constant positive solution existence