On weak solutions of nonlinear weighted p-Laplacian elliptic inequalities

In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class Wloc1,p(Rn)∩C(Rn) of pp-Laplacian elliptic inequalities with possibly singular weights. In order to get the results a new Omori–Yau type principle is used. We complement our nonexistence results by establishing existence of infinitely many positive radial solutions each of which blows up at some finite R>0R>0. Finally, a criterium for the existence of positive entire large radial solutions of class Wloc1,p(Rn)∩C(Rn) is also established.