In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class 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 is also established.
On weak solutions of nonlinear weighted p-Laplacian elliptic inequalities / R. Filippucci, P. Pucci, M. Rigoli. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 70:8(2009), pp. 3008-3019. [10.1016/j.na.2008.12.031]
On weak solutions of nonlinear weighted p-Laplacian elliptic inequalities
M. RigoliUltimo
2009
Abstract
In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class 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 is also established.
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