2010/06/01 by Roberta Filippucci, ROBERTA FILIPPUCCI, Patrizia Pucci +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Boundary value problem #Curvature #Elliptic curve #Geometric Analysis and Curvature Flows #Geometry #Laplace operator #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Nonlinear system #Pure mathematics #Simple (philosophy) #p-Laplacian
paper · doi:10.1142/s0219199710003841
crossref issued 2010/06/01 · crossref published 2010/06/01 · crossref published-print 2010/06/01 · openalex publication_date 2010/06/01 · crossref created 2010/06/28 · crossref published-online 2011/11/20 · crossref deposited 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04 · crossref indexed 2026/08/04
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-2 Du ≥ 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.