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

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  • Xiaozhou Feng
  • Lifeng Li

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 or converges to infinity.

Suggested Citation

  • Xiaozhou Feng & Lifeng Li, 2012. "Uniqueness and Multiplicity of a Prey-Predator Model with Predator Saturation and Competition," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-30, December.
    • Handle: RePEc:hin:jnljam:627419
    DOI: 10.1155/2012/627419
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