论文标题
关于域中非线性椭圆方程的临界点的临界点的数量和位置
On the number and location of critical points of solutions of nonlinear elliptic equations in domains with a small hole
论文作者
论文摘要
在本文中，我们研究以下问题\ begin {equination} \ begin {case}-Δu= f（u）〜＆\ mbox {in} \ω__\ varepsilon，\\ \> 0〜＆\ mbox {in} \partialΩ_\ varepsilon，\ end {cases} \ end {equation}其中$ω__\ varepsilon =ω\ backslash b（p，p，\ varepsilon）$，$ω\ subset r^n $带有$ n \ geq 2 $ in $ n \ geq 2 $是$ bolded in comply in $ bilt in $ ball $ ball $ ball $ ball（半径$ \ varepsilon> 0 $和$ f $是平稳的非线性。 通过一些涉及绿色功能和学位理论的计算，我们计算了小$ \ varepsilon> 0 $的解决方案关键点的数量和位置。
In this paper we study the following problem \begin{equation} \begin{cases} -Δu=f(u)~&\mbox{in}\ Ω_\varepsilon,\\ u>0~&\mbox{in}\ Ω_\varepsilon,\\ u=0~&\mbox{on}\ \partialΩ_\varepsilon, \end{cases} \end{equation} where $Ω_\varepsilon=Ω\backslash B(P,\varepsilon)$, $Ω\subset R^N$ with $N\geq 2$ is a smooth bounded domain, $B(P,\varepsilon)$ is the ball centered at $P$ and radius $\varepsilon>0$ and $f$ is a smooth nonlinearity. By some computations involving the Green function and degree theory, we compute the number and location of critical points of solutions for small $\varepsilon>0$.
