Existence of solutions for some quasilinear $\vec{p}(x)$-elliptic problem with Hardy potential

Abstract

N i=1 D i a i (x, u, ∇u) + |u| s(x)−1 u = f + λ |u| p0(x)−2 u |x| p0(x) in Ω, u = 0 on ∂Ω, where Ω is an open bounded subset of R N containing the origin. We show the existence of entropy solution for this equation where the data f is assumed to be in L 1 (Ω) and λ is a positive constant.