论文标题
涉及操作员等电线的超临界椭圆问题
Supercritical elliptic problems involving a Cordes like operator
论文作者
论文摘要
在这项工作中，我们获得了\ begin {equation}的各种扰动的正界解决方案 \ left \ {\ begin {array} {lcl} \ hfill-ΔU -γ\ sum_ {i，j = 1}^n \ frac {x_i x_j} {| x |^2} | x |^2} u__i x_i x_j} ＆=＆0 \ hfill \ mbox {on} \ partial b_1，\ end {array} \ right。 \ end {equation}其中$ b_1 $是$ \ ir^n $中的单位球，其中$ n \ ge 3 $，$γ> 0 $和$ 1 <p <p <p <p <p_ {n，γ} $ \ begin {equation*} p_ {n，γ}：= \ left \ {\ begin {array} {lc} \ frac {n+2+3γ} {n-2-γ}＆\ qquad \ mbox {if}γ<n-2，\\ \ \ fty＆\ qquad \ qquad \ mbox {if}γ\ ge n-2。 \ end {array} \ right。 \ end {equation*}注意$γ> 0 $，这允许$ p $的超临界范围。
In this work we obtain positive bounded solutions of various perturbations of \begin{equation} \left\{ \begin{array}{lcl} \hfill -Δu - γ\sum_{i,j=1}^N \frac{x_i x_j}{|x|^2} u_{x_i x_j} &=& u^p \qquad \mbox{ in } B_1, \\ \hfill u &=& 0 \hfill \mbox{ on } \partial B_1, \end{array}\right. \end{equation} where $B_1$ is the unit ball in $ \IR^N$ where $N \ge 3$, $ γ>0$ and $ 1<p<p_{N,γ}$ where \begin{equation*} p_{N,γ}:=\left\{ \begin{array}{lc} \frac{N+2+3 γ}{N-2-γ} & \qquad \mbox{ if } γ<N-2, \\ \infty & \qquad \mbox{ if } γ\ge N-2. \end{array}\right. \end{equation*} Note for $γ>0$ this allows for supercritical range of $p$.
