Some Liouville theorems for Henon type elliptic equations

被引：82
|
作者：
Wang, Chao [2 ]
Ye, Dong [1 ]
机构：
[1] Univ Metz, Dept Math, UMR 7122, F-57045 Metz, France
[2] Univ Cergy Pontoise, Dept Math, UMR 8088, F-95302 Cergy Pontoise, France
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 04期
关键词：
Liouville theorem; Henon equation; Stability; Finite Morse index solution; POSITIVE SOLUTIONS; DELTA-U; CLASSIFICATION; STABILITY; E(U);
D O I：
10.1016/j.jfa.2011.11.017
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate here the nonlinear elliptic equations -Delta u = vertical bar x vertical bar(alpha)e(u) and -Delta u = vertical bar x vertical bar(alpha)vertical bar u vertical bar(p-1)u with alpha > -2, p > 1 and N >= 2. In particular, we prove some Liouville type theorems for weak solutions with finite Morse index in the low dimensional Euclidean spaces or half spaces. (C) 2011 Elsevier Inc. All rights reserved.
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页码：1705 / 1727
页数：23
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