American Institute of Mathematical Sciences;American Institute of Mathematical Sciences (AIMS)
摘要:
摘要： In this article, we consider the following semilinear elliptic equation on the hyperbolic space \begin{eqnarray} \Delta_{H^n} u-\lambda u+|u|^{p-1}u=0\quad on\quad H^n\setminus \{Q\} \end{eqnarray} where $\Delta_{H^n}$ is the Laplace-Beltrami operator on the hyperbolic space \begin{eqnarray} H^n=\{(x_1,\cdots, x_n,x_{n+1})|x_1^2+\cdots+x_n^2-x_{n+1}^2=-1\}, \end{eqnarray} $n>10,\ p>1, \lambda>0, $ and $Q=(0,\cdots,0,1)$. 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. 其他題名： CPAA 出版者： American Institute of Mathematical Sciences (AIMS) 出版日期： 2014-03-01 出處： Communications on Pure and Applied Analysis, 2014-03, Vol.13 (2), p.949-960 識別號： ISSN: 1553-5258 識別號： ISSN: 1534-0392 識別號： EISSN: 1553-5258 識別號： DOI: 10.3934/cpaa.2014.13.949
