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Qualitative analysis to an eigenvalue problem of the Hénon equation

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成果类型:
期刊论文
作者:
Luo, Peng;Tang, Zhongwei;Xie, Huafei
通讯作者:
Xie, HF
作者机构:
[Luo, Peng] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
[Tang, Zhongwei] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.
[Xie, Huafei] Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.
通讯机构:
[Xie, HF ] N
Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.
语种:
英文
关键词:
Morse index;Supercritical Henon problem;Local Pohozaev identity
期刊:
Journal of Functional Analysis
ISSN:
0022-1236
年:
2024
卷:
286
期:
2
页码:
110206
基金类别:
National Natural Science Foundation of China [12201232]; Fundamental Research Funds for the Central Universities [KJ02072020-0319, CCNU22LJ002]
机构署名:
本校为第一机构
院系归属:
数学与统计学学院
摘要:
In this paper we study the following eigenvalue problem {-Delta v = lambda C(alpha)(p(alpha) - epsilon)vertical bar x vertical bar(alpha)u(epsilon)(p alpha-epsilon-1)v in Omega, u=0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain containing the origin, C(alpha) = (N + alpha)(N - 2), N >= 3, p(alpha) = N+2+2 alpha/N-2, alpha > 0, epsilon > 0 is a small parameter and u(epsilon) is a single peaked solution of Henon equation {-Delta u = C(alpha)vertical bar x vertical bar(alpha)u(p alpha-epsilon) in Omega, u > 0 in Omega, u=0 on partial derivative Omega, which est...

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