On the existence of positive solutions for an ecological model with indefinite weight

Abstract

This study concerns the existence of positive solutions for the following nonlinear boundary value problem: {−Δu=am(x)u−bu2−cupup+1−Kin Ω,u=0on ∂Ω, where Δu=div(∇u) is the Laplacian of u, while a,b,c,p,K are positive constants with p≥2 and Ω is a bounded smooth domain of RN with ∂Ω in C2. The weight function m satisfies m∈C(Ω) and m(x)≥m0>0 for x∈Ω, also ‖m‖∞=l<∞. We prove the existence of positive solutions under certain conditions.

Keywords

• Ecological systems
• Indefinite weight
• Grazing and constant yield harvesting
• Sub–super solution method