论文标题
$ f'（u^\ ast）$的起源附近的行为在径向奇异的极端解决方案中
Behavior near the origin of $f'(u^\ast)$ in radial singular extremal solutions
论文作者
论文摘要
考虑单位球中的半连续性椭圆方程$-ΔU=λf（u）$ $ b_1 \ subset \ subset \ mathbb {r}^n $，带有dirichlet data $ u | _ {\ partial b_1} = 0 $ $ [0，\ infty）$，以至于$ f（s）/s \ rightarrow \ infty $ as $ s \ rightarrow \ infty $。在本文中，我们研究了$ f'（u^\ ast）$附近的行为时，当$ u^\ ast $，这是与$λ=λ^\ ast $相关的先前问题的极端解决方案，这是单数。这回答了布雷兹斯和瓦兹克斯带来的开放问题。
Consider the semilinear elliptic equation $-Δu=λf(u)$ in the unit ball $B_1\subset \mathbb{R}^N$, with Dirichlet data $u|_{\partial B_1}=0$, where $λ\geq 0$ is a real parameter and $f$ is a $C^1$ positive, nondecreasing and convex function in $[0,\infty)$ such that $f(s)/s\rightarrow\infty$ as $s\rightarrow\infty$. In this paper we study the behavior of $f'(u^\ast)$ near the origin when $u^\ast$, the extremal solution of the previous problem associated to $λ=λ^\ast$, is singular. This answers to an open problems posed by Brezis and Vázquez.
