A strong maximum principle for a class of non-positone singular elliptic problems

Damascelli, Lucio ; Pacella, Filomena ; Ramaswamy, Mythily (2003) A strong maximum principle for a class of non-positone singular elliptic problems Nonlinear Differential Equations and Applications, 10 (2). pp. 187-196. ISSN 1021-9722

[img]
Preview
PDF - Author Version
216kB

Official URL: http://www.springerlink.com/content/7dbrnt1457a5nn...

Related URL: http://dx.doi.org/10.1007/s00030-003-1007-z

Abstract

We prove that nonnegative solutions of quasilinear elliptic problems of the type (0.1) {-Δpu=f(u) in Ω, 1 < p ≤ 2 u = 0 on ∂Ω are actually positive in Ω , under the following assumptions: Ω is a regular bounded strictly convex domain in ,RN,N ≥ 2 symmetric with respect to a hyperplane, ƒ is a locally Lipschitz continuous function in [0,+ ∞) with ƒ(0) <0, and u is a weak solution in C1(Ω̅). The proof of this result uses the moving plane method as in [2] and can be adapted to more general geometric situations.

Item Type:Article
Source:Copyright of this article belongs to Springer.
ID Code:62290
Deposited On:20 Sep 2011 09:31
Last Modified:18 May 2016 11:39

Repository Staff Only: item control page