Semilinear elliptic equations with degenerate and singular weights related to Caffarelli–Kohn–Nirenberg inequalities

Abstract

In this note we give some existence and nonexistence results of solutions to a problem of the type (Pt,p){−div(|x|−2γ∇u)=λ|x|2(γ+1)u+up|x|α+tf|x|2γin Ωu≥0,u≢0in Ωu=0on ∂Ω, where Ω is an open bounded subset of RN containing the origin, the constants p,t,α,γ,λ satisfy suitable conditions and f≢0 is a nonnegative, smooth bounded function on Ω. The results that will be given generalize some known results in Brezis et al. (2005) [1] and Dupaigne (2002) [2].