On a p-Kirchhoff-type problem arising in ecosystems

Abstract In this article, we discuss the existence of positive solutions for an ecological model of the form: {−M(∫Ω∣∇u∣pdx)Δpu=aup−1−buγ−1−cuα,u=0,x∈Ω,x∈∂Ω, where Ω is a bounded domain with smooth boundary, Δpu=div(|∇u|p−2∇u),10,b>0,c≥0, and α∈(0,1). This model describes the steady states of a logistic growth model with grazing and constant yield harvesting. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. We discuss the existence of a positive solution for given a,b,γ and small values of c.