论文标题
关于罗宾功能的临界点的定性分析
Qualitative analysis on the critical points of the Robin function
论文作者
论文摘要
令$ n \ ge2 $和$ n \ ge2 $和$ω_____________________\ backslash b（p，ε）$，其中$ b（p，ε）$是$ p \ incy $ incy $和radius $ε$。在本文中，我们建立了罗宾功能的关键点的数量，位置和非分数，以$ω_ε$为$ε$，$ε$足够小。我们将证明$ p $的位置在关键点的存在和多重性上起着至关重要的作用。我们结果的证明是对绿色功能接近$ \ a部分b（p，ε）$的微妙估计的结果。将显示一些用于计算相关良好的非线性椭圆问题的确切解决方案数量的应用。
Let $Ω\subset\mathbb{R}^N$ be a smooth bounded domain with $N\ge2$ and $Ω_ε=Ω\backslash B(P,ε)$ where $B(P,ε)$ is the ball centered at $P\inΩ$ and radius $ε$. In this paper, we establish the number, location and non-degeneracy of critical points of the Robin function in $Ω_ε$ for $ε$ small enough. We will show that the location of $P$ plays a crucial role on the existence and multiplicity of the critical points. The proof of our result is a consequence of delicate estimates on the Green function near to $\partial B(P,ε)$. Some applications to compute the exact number of solutions of related well-studied nonlinear elliptic problems will be showed.
