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

摘要

This paper deals with the existence and nonexistence results for quasilinear elliptic equations of the form -Δ_pu = f(x, u), where Δ_p:=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) = u~p|x|~(-p), that is related to a classical Hardy inequality.