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

被引：21

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

共 24 条

[1] Some remarks on elliptic problems with critical growth in the gradient [J].

Abdellaoui, B ;

Dall'Aglio, A ;

Peral, I .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 222 (01) :21-62

[2]

Abdellaoui B., 2007, ANN SC NORM SUPE S 5, VVI, P1

[3] Elliptic problems with a Hardy potential and critical growth in the gradient: Non-resonance and blow-up results [J].

Abdellaoui, Boumediene ;

Peral, Ireneo ;

Primo, Ana .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 239 (02) :386-416

[4] WEAK SOLUTIONS OF SOME QUASI-LINEAR ELLIPTIC-EQUATIONS WITH DATA MEASURES [J].

ALAA, NE ;

PIERRE, M .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (01) :23-35

[5]

Azorero JPG, 1998, J DIFFER EQUATIONS, V144, P441

[6]

Benilan P., 1995, Ann. Scuola Norm. Sup. Pisa Cl. Sci, V22, P241

[7] ALMOST EVERYWHERE CONVERGENCE OF THE GRADIENTS OF SOLUTIONS TO ELLIPTIC AND PARABOLIC EQUATIONS [J].

BOCCARDO, L ;

MURAT, F .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (06) :581-597

[8] Existence and nonexistence of solutions for some nonlinear elliptic equations [J].

Boccardo, L ;

Gallouet, T ;

Orsina, L .

JOURNAL D ANALYSE MATHEMATIQUE, 1997, 73 (1) :203-223

[9]

Boccardo L., 1984, ANN SC NORM SUP PISA, V11, P213

[10]

Boccardo L., 1983, RES NOTES MATH, V84, P19

← 1 2 3 →