Existence Results in Weighted Sobolev Space for Quasilinear Degenerate P(z)−elliptic Problems With a Hardy Potential

The objective of this work is to establish the existence of entropy solutions to degenerate nonlinear elliptic problems for L¹-data f with a Hardy potential, in weighted Sobolev spaces with variable exponent, which are represented as follows {gather*} -div(Φ(z,v,∇ v))+g(z,v,∇ v)=f+ρ{ v ᵖ⁽ᶻ⁾⁻²v}{|v|ᵖ⁽ᶻ⁾}, {gather*} where -div(Φ(z,v,∇ v)) is a Leray-Lions operator from W₀1,p(z)(Ω,ω) into its dual, g(z,v,∇ v) is a non-linearity term that only meets the growth condition, and ρ>0 is a constant.