On weak solutions of nonlinear weighted p-Laplacian elliptic inequalities

Abstract

In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class W loc 1 , p ( R n ) ∩ C ( R n ) of p -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 > 0 . Finally, a criterium for the existence of positive entire large radial solutions of class W loc 1 , p ( R n ) ∩ C ( R n ) is also established.