Existence and nonexistence of solutions for singular quadratic quasilinear equations

被引：100

作者：

Arcoya, David ^{[1
]}

Carmona, Jose ^{[2
]}

Leonori, Tommaso ^{[3
]}

Martinez-Aparicio, Pedro J. ^{[1
]}

Orsina, Luigi ^{[4
]}

Petitta, Francesco ^{[5
]}

机构：

[1] Univ Granada, Dept Anal Matemat, E-18071 Granada, Spain

[2] Univ Almeria, Dept Algebra & Anal Matemat, La Canada De San Urbano 04120, Almeria, Spain

[3] Univ Coimbra, Dept Math, CMUC, P-3001454 Coimbra, Portugal

[4] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[5] Univ Oslo, CMA, NO-0316 Oslo, Norway

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 10期

关键词：

Nonlinear elliptic equations; Singular natural growth gradient terms; Large solutions; NONLINEAR ELLIPTIC-EQUATIONS; NATURAL GROWTH TERMS; PARABOLIC EQUATIONS; ASYMPTOTIC-BEHAVIOR; GRADIENT TERM; BLOW-UP; UNIQUENESS; BOUNDARY; INFINITY;

D O I：

10.1016/j.jde.2009.01.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with Singular lower order terms that have natural growth with respect to the gradient, whose model is {-Delta u + vertical bar del u vertical bar(2)/u(gamma) = f in Omega. u = 0 on partial derivative Omega. where Omega is an open bounded subset of R, gamma > 0 and f is a function which is strictly positive on every compactly contained subset of Omega. As a consequence of our main results, we prove that the condition gamma < 2 is necessary and sufficient for the existence of solutions in H-0(1) (Omega) for every sufficiently regular f as above. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：4006 / 4042

页数：37

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[2]

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[3]

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[4]

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