论文标题
Brezis-Nirenberg问题的节点解决方案6
Nodal solutions of the Brezis-Nirenberg problem in dimension 6
论文作者
论文摘要
我们证明了经典的Brezis -Nirenberg问题$$-ΔU= U | U | +λu\ \ hbox {in} \ω， u = 0 \ \ hbox {on} \ \partialΩ， $$当$ω$是$ \ mathbb r^6 $中的一个有界域时具有签名的解决方案，该解决方案以$ω$为$ω$ aS $λ$接近$λ_0> 0。
We show that the classical Brezis-Nirenberg problem $$ -Δu=u|u| + λu\ \hbox{in}\ Ω, u=0\ \hbox{on}\ \partialΩ, $$ when $Ω$ is a bounded domain in $\mathbb R^6$ has a sign-changing solution which blows-up at a point in $Ω$ as $λ$ approaches a suitable value $λ_0>0.$
