Existence, nonexistence and asymptotic behavior of boundary blow-up solutions to p(x)-Laplacian problems with singular coefficient

被引：11

作者：

Zhang, Qihu ^{[1
]}

机构：

[1] Zhengzhou Univ Light Ind, Dept Math & Informat Sci, Zhengzhou 450002, Henan, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 06期

基金：

美国国家科学基金会; 中国博士后科学基金;

关键词：

p(x)-Laplacian; Sub-solution; Super-solution; Singularity; ELLIPTIC-EQUATIONS; VARIABLE EXPONENT; DIFFERENTIAL-EQUATIONS; UNIQUENESS; REGULARITY; SPACES; FUNCTIONALS; GRADIENT;

D O I：

10.1016/j.na.2010.10.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the problem {-Delta(p(x))u + rho(x)f(x, u) = 0 in Omega, u(x) -> +infinity as d(x, partial derivative Omega) -> 0, where -Delta(p(x))u = -div(vertical bar del u vertical bar(p(x)-2)del u) is called the p(x)-Laplacian, and rho(x) is a singular coefficient. The existence and nonexistence of boundary blow-up solutions is discussed, and the asymptotic behavior of boundary blow-up solutions is given. In particular, we do not assume radial symmetric conditions, and the pointwise different exact blow-up rate of solutions has been discussed. Published by Elsevier Ltd

引用

页码：2045 / 2061

页数：17

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