论文标题
低维度的勃雷齐斯·尼伦贝格问题的淋巴结径向解决方案的完整情况
A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions
论文作者
论文摘要
在本文中，我们考虑问题的鼻径向解决方案$$ \ begin {case}-ΔU= | | |^{2^* - 2} u+++λu＆\ text {in} b，\\ u = 0＆\ u = 0＆\ text {on} n \ le6 $和$ b $是$ \ r^n $的单位球。我们计算解决方案$ u $的渐近学以及$ || u || _ \ infty $，其第一个零和其他相关数量，因为$ $ $ to to to to Critist to Critical Value $ \barł$。在所有情况下，均建立了$ - \barł$的标志。 这完成了[EGPV]中给出的$ n \ ge7 $的类似分析。
In this paper we consider nodal radial solutions of the problem $$ \begin{cases} -Δu=|u|^{2^*-2}u+λu&\text{ in }B,\\ u=0&\text{ on }\partial B \end{cases} $$ where $2^*=\frac{2N}{N-2}$ with $3\le N\le6$ and $B$ is the unit ball of $\R^N$. We compute the asymptotics of the solution $u$ as well as $||u||_\infty$, its first zero and other relevant quantities as $ł$ goes to a critical value $\barł$. Also the sign of $ł-\barł$ is established in all cases. This completes an analogous analysis for $N\ge7$ given in [EGPV].
