Non-radial least energy solutions of the generalized Henon equation

被引：19
|
作者：
Kajikiya, Ryuji [1 ]
机构：
[1] Saga Univ, Fac Sci & Engn, Dept Math, Saga 8408502, Japan
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 252卷 / 02期
基金：
日本学术振兴会;
关键词：
Henon equation; Positive solution; Least energy solution; Non-radial solution; Variational method; SUBLINEAR ELLIPTIC-EQUATIONS; GROUND-STATES; ASYMPTOTIC PROFILE; POSITIVE SOLUTIONS; MAXIMUM PRINCIPLE; UNIQUENESS; GROWTH;
D O I：
10.1016/j.jde.2011.08.032
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the generalized Henon equation with a radial coefficient function in the unit ball and show the existence of a positive non-radial solution. Our result is applicable to a wide class of coefficient functions. Our theorem ensures that if the ratio of the density of the coefficient function in vertical bar x vertical bar < a to that in a < vertical bar x vertical bar < 1 is small enough and a is sufficiently close to 1, then a least energy solution is not radially symmetric. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：1987 / 2003
页数：17
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