Uniqueness and Multiplicity of a Prey-Predator Model with Predator Saturation and Competition

Abstract EN

We investigate positive solutions of a prey-predator model withpredator saturation and competition under homogeneous Dirichlet boundary conditions.

First,the existence of positive solutions and some sufficient and necessary conditions is established byusing the standard fixed point index theory in cones.

Second, the changes of solution branches,multiplicity, uniqueness, and stability of positive solutions are obtained by virtue of bifurcationtheory, perturbation theory of eigenvalues, and the fixed point index theory.

Finally, the exactnumber and type of positive solutions are proved when k or m converges to infinity.