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

The paper is concerned with a predator-prey diffusive dynamicssubject 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.