## Journal of Applied Mathematics

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

#### Abstract

We investigate 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 is 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.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 627419, 30 pages.

Dates
First available in Project Euclid: 7 May 2014

https://projecteuclid.org/euclid.jam/1399490202

Digital Object Identifier
doi:10.1155/2012/627419

Mathematical Reviews number (MathSciNet)
MR3005230

Zentralblatt MATH identifier
1263.92045

#### Citation

Feng, Xiaozhou; Li, Lifeng. Uniqueness and Multiplicity of a Prey-Predator Model with Predator Saturation and Competition. J. Appl. Math. 2012 (2012), Article ID 627419, 30 pages. doi:10.1155/2012/627419. https://projecteuclid.org/euclid.jam/1399490202