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- Title
NONLINEAR WEIGHTED p-LAPLACIAN ELLIPTIC INEQUALITIES WITH GRADIENT TERMS.
- Authors
FILIPPUCCI, ROBERTA; PUCCI, PATRIZIA; RIGOLI, MARCO
- Abstract
In this paper, we give sufficient conditions for the existence and nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div{g(|x|)|Du|p-2Du} ≥ h(|x|)f(u)ℓ(|Du|). We achieve our conclusions by using a generalized version of the well-known Keller–Ossermann condition, first introduced in [2] for the generalized mean curvature case, and in [11, Sec. 4] for the nonweighted p-Laplacian equation. Several existence results are also proved in Secs. 2 and 3, from which we deduce simple criteria of independent interest stated in the Introduction.
- Subjects
LAPLACIAN operator; PARTIAL differential equations; CALCULUS; MATHEMATICAL analysis; INFINITESIMAL geometry
- Publication
Communications in Contemporary Mathematics, 2010, Vol 12, Issue 3, p501
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199710003841