Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space

Yen Lin Wu, Zhi You Chen, Jann Long Chern, Yoshitsugu Kabeya

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this article, we consider the following semilinear elliptic equation on the hyperbolic space ΔHnu - λu + |u|p-1u = 0 on Hn n\{Q} where ΔHn is the Laplace-Beltrami operator on the hyperbolic space Hn = {(x 1, · · · xn, xn+1)|x 12 + · · · + xn 2 - x n+1 2 = -1}, n > 10, p > 1, λ > 0, and Q = (0, · · · 0, 1). We provide the existence and uniqueness of a singular positive "radial" solution of the above equation for big p (greater than the Joseph-Lundgren exponent, which appears if n > 10) as well as its asymptotic behavior.

原文英語
頁(從 - 到)949-960
頁數12
期刊Communications on Pure and Applied Analysis
13
發行號2
DOIs
出版狀態已發佈 - 2014 三月
對外發佈

ASJC Scopus subject areas

  • 分析
  • 應用數學

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