J4 ›› 2011, Vol. 46 ›› Issue (2): 15-21.
• Articles •
JIANG Liang-zhan, LI Yan-ling*
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.
prey refuge; priori estimate; non-constant positive solution existence
JIANG Liang-zhan, LI Yan-ling*. Existence of positive non-constant steady-states to a predator-prey system incorporating a constant prey refuge[J].J4, 2011, 46(2): 15-21.
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