NONEXISTENCE FOR P-LAPLACE EQUATIONS WITH SINGULAR WEIGHTS

Aim of this paper is to give some nonexistence results of nontrivial solutions for a quasilinear elliptic equations with singular weights in R^n / {0}. The main tool for deriving nonexistence theorems for the equations is a Pohoaev-type identity. We first show that such identity holds true for weak solutions sufficiently smooth. Then, under a suitable growth condition on the nonlinearity, we prove that every weak solution has thhe required regularity, so that the Pohosaev-type identity can be applied. From this identity we derive some nonexistence results, improving several theorems already appeared in the literature. In particular, we discuss the case when h and f are pure powers