Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations

被引：20

作者：

Abdellaoui, Boumediene ^{[2
]}

Peral, Ireneo ^{[1
]}

Primo, Ana ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Dept Math, E-28049 Madrid, Spain

[2] Univ Aboubekr Belkaid, Dept Math, Tilimsen 13000, Tlemcen, Algeria

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2008年 / 25卷 / 05期

关键词：

Quasilinear elliptic equations; Existence and nonexistence; Regularization; Resonance;

D O I：

10.1016/j.anihpc.2007.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study the problem (P) {-Delta u + vertical bar del u vertical bar(q) = lambda g(x)u + f(x) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, with 1 <= q <= 2 and f, g are positive measurable functions. We give assumptions on g with respect to q for which for all lambda > 0 and all f is an element of L-1, f >= 0, problem (P) has a positive solution. In particular we focus our attention on g(x) = 1/vertical bar x vertical bar(2) to prove that the assumptions on g are optimal. (C) 2007 Elsevier Masson SAS. All rights reserved.

引用

页码：969 / 985

页数：17

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