Existence and nonexistence results for quasilinear elliptic equations involving the p-laplacian with a critical potential

Abstract

This paper deals with the existence and nonexistence results for quasilinear elliptic equations of the form -Δpu = f(x, u), where Δp:= div(|∇u|p-2∇u), p > 1, and the solutions are understood in the sense of renormalized or, equivalently, entropy solutions. In particular we prove nonexistence results in the case f(x, u) = up|x|-p, that is related to a classical Hardy inequality.