# American Institute of Mathematical Sciences

May  2015, 14(3): 1183-1204. doi: 10.3934/cpaa.2015.14.1183

## Some uniqueness and multiplicity results for a predator-prey dynamics with a nonlinear growth rate

 1 College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shannxi 710062, China 2 College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710119 3 College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710062

Received  August 2014 Revised  January 2015 Published  March 2015

The paper is concerned with a predator-prey diffusive dynamics subject to homogeneous Dirichlet boundary conditions, in which the growth rate of the the predator is nonlinear. Taking $m$ as the main parameter, we show the existence, stability and exact number of positive solution when $m$ is large, and some numerical simulations are done to complement the analytical results. The main tools used here include the fixed point index theory, the super-sub solution method, the bifurcation theory and the perturbation technique.
Citation: Wen-Bin Yang, Jianhua Wu, Hua Nie. Some uniqueness and multiplicity results for a predator-prey dynamics with a nonlinear growth rate. Communications on Pure & Applied Analysis, 2015, 14 (3) : 1183-1204. doi: 10.3934/cpaa.2015.14.1183
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