Nondegeneracy of solutions to the critical p$p$ ‐Laplace Kirchhoff equation
Nondegeneracy of solutions to the critical p$p$ ‐Laplace Kirchhoff equation
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DOI：
10.1112/blms.12839
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发表时间：
2023-04
影响因子：
0.9
通讯作者：
Shengbing Deng;Xingliang Tian
中科院分区：
文献类型：
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作者：
Shengbing Deng;Xingliang Tian
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We establish the nondegeneracy of solutions in suitable space to the following p$p$ ‐Laplace Kirchhoff equation with critical Sobolev exponent: −1+b∫RN|∇u|pdxdiv(|∇u|p−2∇u)=up*−1,u>0inRN,$$\begin{eqnarray*} &&\hspace*{80pt} -{\left(1+b\int _{\mathbb {R}^N}|\nabla u|^p dx\right)} {\rm div}(|\nabla u|^{p-2}\nabla u)=u^{p^\ast -1},\hspace*{-80pt}\\ &&\hspace*{80pt} u>0\quad \mbox{in}\quad \mathbb {R}^N,\hspace*{-80pt} \end{eqnarray*}$$where b>0$b>0$ , 12p$N>2p$ , that is, we show that there exist two nondegenerate solutions that seem to be completely different from the result of critical p$p$ ‐Laplace equation ( b=0$b=0$ ) or the low‐dimensional Kirchhoff equation (the case p