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  has studied this system for large β under the restriction b > (1 + γ)λ1, where λ1 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.
|ジャーナル||Differential and Integral Equations|
|出版ステータス||Published - 2009 7 1|
ASJC Scopus subject areas
- Applied Mathematics