Classification of finite Morse index solutions to the polyharmonic Henon equation

被引:0
作者
Ao, Weiwei [1 ]
Lai, Shanshan [1 ]
Luo, Senping [2 ]
机构
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
[2] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China
关键词
LIOUVILLE-TYPE THEOREMS; ENERGY ENTIRE SOLUTIONS; ELLIPTIC-EQUATIONS; LOCAL BEHAVIOR;
D O I
10.1007/s00526-022-02361-x
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present Liouville-type results for stable solutions and finite Morse index solutions of the polyharmonic Henon elliptic equation (-Delta)(m)u = vertical bar x vertical bar(a)vertical bar u vertical bar(p-1)u, in R-n, where m >= 3, p>1, a >= 0 and n is a large dimension. To construct the classification theorem of homogeneous stable solutions, we exhibit a concise and explicit form for a critical exponent p(a)(n,m) which is known as the Joseph-Lundgren exponent when taking a=0. Based on this, we obtain the desired results by establishing the monotonicity formula, applying some energy estimates and finally using a blow-down analysis.
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页数:50
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