J4 ›› 2011, Vol. 46 ›› Issue (2): 15-21.

• Articles • Previous Articles     Next Articles

Existence of positive non-constant steady-states to a predator-prey system incorporating a constant prey refuge

JIANG Liang-zhan, LI Yan-ling*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China
  • Received:2009-10-26 Online:2011-02-16 Published:2011-03-30


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

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