Morse指数与带权的椭圆方程的Liouville型定理

数学物理学报 ›› 2016, Vol. 36 ›› Issue (3): 493-499.

Morse指数与带权的椭圆方程的Liouville型定理

肖迎迎, 郑雄军

江西师范大学数学系南昌 330022

收稿日期:2015-10-11 修回日期:2016-03-23 出版日期:2016-06-26 发布日期:2016-06-26
作者简介:肖迎迎,ying1ying4xiao@sina.com;郑雄军,xjzh1985@126.com
基金资助:
国家自然科学基金（11271170）和赣鄱英才555工程资助

Morse Indices and Liouville Type Theorems for Weighted Elliptic Equations

Xiao Yingying, Zheng Xiongjun

Department of Mathematics, Jiangxi Normal University, Nanchang 330022

Received:2015-10-11 Revised:2016-03-23 Online:2016-06-26 Published:2016-06-26
Supported by:
Supported by the NSFC (11271170) and Gan-Po Talent 555 Project of Jiangxi Province

摘要/Abstract

摘要：

该文研究全空间R^N上带权的半线性椭圆型方程
-Δu=|x|^α|u|^p-1u，x∈R^N
与半空间R₊^N=｛x∈R^N: x_N >0｝上带权的半线性椭圆型问题
-Δu=|x|^α|u|^p-1u，x∈R₊^N，u|_∂R₊^N=0
的Liouville型定理，其中N ≥ 3，α > -2. 证明了，当1 < p < (N+2α+2)/(N-2)时，上述问题的Morse指数有限的有界解只能是零解.

关键词: Morse指数, Liouville型定理

Abstract:

This paper is concerned with Liouville type theorems for weighted semilinear elliptic equations
-Δu=|x|^α|u|^p-1u,x∈R^N
and
-Δu=|x|^α|u|^p-1u,x∈R₊^N,u|_∂R₊^N=0,
where N ≥ 3 and α>-2. We prove that the bounded solutions of the above problems with finite Morse indices are zero when 1 < p < (N+2α+2)/(N-2).

Key words: Morse indices, Liouville type theorems

中图分类号:

O175.25

肖迎迎, 郑雄军. Morse指数与带权的椭圆方程的Liouville型定理[J]. 数学物理学报, 2016, 36(3): 493-499.

Xiao Yingying, Zheng Xiongjun. Morse Indices and Liouville Type Theorems for Weighted Elliptic Equations[J]. Acta mathematica scientia,Series A, 2016, 36(3): 493-499.

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