Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4618100 | Journal of Mathematical Analysis and Applications | 2011 | 10 Pages |
Abstract
We consider the existence of multiple positive solutions to the steady state reaction diffusion equation with Dirichlet boundary conditions of the form:{−Δu=λ[u−u2K−cu21+u2],x∈Ω,u=0,x∈∂Ω. Here Δu=div(∇u)Δu=div(∇u) is the Laplacian of u , 1λ is the diffusion coefficient, K and c are positive constants and Ω⊂RNΩ⊂RN is a smooth bounded region with ∂Ω in C2C2. This model describes the steady states of a logistic growth model with grazing in a spatially homogeneous ecosystem. It also describes the dynamics of the fish population with natural predation. In this paper we discuss the existence of multiple positive solutions leading to the occurrence of an S-shaped bifurcation curve. We prove our results by the method of sub-supersolutions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Eunkyoung Lee, Sarath Sasi, R. Shivaji,