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Positive Solutions of a Diffusive Predator-Prey System including Disease for Prey and Equipped with Dirichlet Boundary Condition

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  • Xiaoqing Wen
  • Yue Chen
  • Hongwei Yin

Abstract

We study a three-dimensional system of a diffusive predator-prey model including disease spread for prey and with Dirichlet boundary condition and Michaelis-Menten functional response. By semigroup method, we are able to achieve existence of a global solution of this system. Extinction of this system is established by spectral method. By using bifurcation theory and fixed point index theory, we obtain existence and nonexistence of inhomogeneous positive solutions of this system in steady state.

Suggested Citation

  • Xiaoqing Wen & Yue Chen & Hongwei Yin, 2016. "Positive Solutions of a Diffusive Predator-Prey System including Disease for Prey and Equipped with Dirichlet Boundary Condition," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-10, October.
    • Handle: RePEc:hin:jnddns:2323752
    DOI: 10.1155/2016/2323752
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