### Abstract

We consider the following quasilinear elliptic system: (EQUATION PRESENT) where Ω is a bounded domain in ℝ. This system is a stationary problem of a prey-predator model with non-linear diffusion δ(^{v}/ _{1+βu} ), and u (respectively v) denotes the population density of the prey (respectively the predator). Kuto [15] has studied this system for large β under the restriction b > (1 + γ)λ_{1}, where λ_{1} is the least eigenvalue of -δ with homogeneous Dirichlet boundary condition. The present paper studies two shadow systems and gives the complete limiting characterization of positive solutions as β → ∞ without any restriction on b.

Original language | English |
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Pages (from-to) | 725-752 |

Number of pages | 28 |

Journal | Differential and Integral Equations |

Volume | 22 |

Issue number | 7-8 |

Publication status | Published - 2009 Jul 1 |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Kuto, K., & Yamada, Y. (2009). Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type.

*Differential and Integral Equations*,*22*(7-8), 725-752.