Uniqueness and multiplicity of a prey-predator model with predator saturation and competition (Q1952900)

Summary: We investigate the positive solutions of a prey-predator model with predator saturation and competition under homogeneous Dirichlet boundary conditions. First, the existence of positive solutions and some sufficient and necessary conditions are established by using 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 bifurcation theory, perturbation theory of eigenvalues, and the fixed point index theory. Finally, the exact number and type of positive solutions are proved when \(k\) or \(m\) converges to infinity.