Large solutions for the Laplacian with a power nonlinearity given by a variable exponent

被引：14

作者：

Garcia-Melian, Jorge ^{[2
]}

Rossi, Julio D. ^{[1
]}

Sabina de Lis, Jose C. ^{[2
]}

机构：

[1] IMDEA Matemat, Madrid, Spain

[2] Univ La Laguna, Dpto Anal Matemat, San Cristobal la Laguna 38271, Spain

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 03期

关键词：

Large solutions; Existence and uniqueness; Variable exponents; BOUNDARY BLOW-UP; SEMILINEAR ELLIPTIC-EQUATIONS; ASYMPTOTIC-BEHAVIOR; EXPLOSIVE SOLUTIONS; UNIQUENESS; EXISTENCE; WEIGHTS;

D O I：

10.1016/j.anihpc.2008.03.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider positive boundary blow-up solutions to the problem Delta u = u(q(x)) in a smooth bounded domain Omega subset of R-n. The exponent q(x) is allowed to be a variable positive Holder continuous function. The issues of existence, asymptotic behavior near the boundary and uniqueness of positive solutions are considered. Furthermore, since q(x) is also allowed to take values less than one, it is shown that the blow up of solutions on partial derivative Omega is compatible with the occurrence of dead cores, i.e., nonempty interior regions where solutions vanish. (C) 2008 Elsevier Masson SAS. All rights reserved.

引用

页码：889 / 902

页数：14

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