A Population biological model with a singular nonlinearity and Caffarelli-Kohn-Nirenberg exponents

Document Type : Research Articles

Author

Ayatollah Amoli Branch, Islamic Azad University

10.22080/cjms.2024.21918.1592

Abstract

We consider the existence of positive solutions of singular nonlinear semipositone problem of the form {−div(|x|−αp|∇u|p−2∇u)=|x|−(α+1)p+β(aup−1−bur−f(u)−cuγ),x∈Ω,u=0,x∈∂Ω,
where Ω is a bounded domain in RN with smooth boundary ∂Ω, 1<p<N, 0≤α<N−pp,r>p−1,γ∈(0,1), a,b,c,β are positive parameters, and f:[0,+∞)→R is a continuous function . This model arises in the studies of population biology of one species
with u representing the concentration of the species. We obtain our results via the method of sub and supersolutions.

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