Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation

被引：25
作者：
Guo, Zongming [1 ]
Wei, Juncheng [2 ]
Zhou, Feng [3 ,4 ]
机构：
[1] Henan Normal Univ, Dept Math, Xinxiang 453007, Peoples R China
[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
[3] East China Normal Univ, Ctr PDEs, Shanghai 200241, Peoples R China
[4] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Radial singular entire solutions; Biharmonic equations; Solutions with prescribed isolated singularities; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; LOCAL BEHAVIOR; DELTA-U; NONLINEARITY; CONSTRUCTION; EXISTENCE; METRICS;
D O I：
10.1016/j.jde.2017.03.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular set for the Navier boundary value problem Delta(2)u = u(p) in Omega, u = Delta u = 0 on partial derivative Omega where Omega is a smooth open set of R-n with n >= 5. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：1188 / 1224
页数：37
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