Large solutions for quasilinear elliptic equation with nonlinear gradient term

被引：9

作者：

Chen, Yujuan ^{[2
]}

Wang, Mingxin ^{[1
]}

机构：

[1] Harbin Inst Technol, Nat Sci Res Ctr, Harbin 150080, Peoples R China

[2] Nantong Univ, Dept Math, Nantong 226007, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 01期

关键词：

Boundary value problems for second order elliptic equations; Asymptotic behavior of solutions; Large solutions; Existence; Uniqueness; Nonlinear gradient term; BLOW-UP SOLUTIONS; ASYMPTOTIC-BEHAVIOR; SINGULAR EQUATIONS; BIEBERBACH;

D O I：

10.1016/j.nonrwa.2010.06.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence, asymptotic behavior near the boundary and uniqueness of large solutions for a class of quasilinear elliptic equation with a nonlinear gradient term. By constructing the suitable blow-up upper and lower solutions, we obtain the existence and the asymptotic behavior of radial large solutions of the problem in balls and then derive the existence of solutions in a general domain by a comparison argument. By using a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of any nonnegative solution of it near the boundary. The uniqueness is shown by a standard argument. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：455 / 463

页数：9

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