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

This paper deals with the existence and nonexistence results for quasilinear elliptic equations of the form -_pu=f(x, u), where _p:=div(|u|^p-2u), 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. Mathematics Subject Classification (2000) 35D05, 35D10, 35J20, 35J25, 35J70