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 p-Laplacian elliptic inequalities with possibly singular weights. In order to get the results a new Omori and 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 > 0. Finally, a criterium for the existence of positive entire large radial solutions is also established.