标题： 二维中Lane-Emden问题的渐近分析 显示英文标题

标题： Asymptotic analysis for the Lane-Emden problem in dimension two

摘要： 我们考虑当$p>1$和$\Omega\subset\mathbb R^2$是一个光滑有界区域时的Lane-Emden狄利克雷问题\begin{equation}\tag{1} \left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }\Omega u=0\qquad\qquad\qquad\mbox{ on }\partial \Omega \end{array}\right. \end{equation}。 本文的目的是综述一些关于当指数$p\rightarrow \infty $时，(1)解的渐近行为的最新结果。 显示英文摘要

摘要： We consider the Lane-Emden Dirichlet problem \begin{equation}\tag{1} \left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }\Omega u=0\qquad\qquad\qquad\mbox{ on }\partial \Omega \end{array}\right. \end{equation} when $p>1$ and $\Omega\subset\mathbb R^2$ is a smooth bounded domain. The aim of the paper is to survey some recent results on the asymptotic behavior of solutions of (1) as the exponent $p\rightarrow \infty $.