Normalized solutions for p-Laplacian equations with a $$L^{2}$$-supercritical growth
Normalized solutions for p-Laplacian equations with a $$L^{2}$$-supercritical growth
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DOI：
10.1007/s43034-020-00101-w
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发表时间：
2020-11
影响因子：
1
通讯作者：
Wenbo Wang;Quanqing Li;Jianwen Zhou;Yongkun Li
中科院分区：
文献类型：
--
作者：
Wenbo Wang;Quanqing Li;Jianwen Zhou;Yongkun Li
我们关注下面的p-拉普拉斯方程$$\begin{aligned} -\varDelta _{p} u+|u|^{p-2}u=\mu u+|u|^{s-2}u,~\text {in}~{\mathbb {R}}^{N}, \end{aligned}$$，其中，，，，是临界索博列夫指数。利用约束变分方法，证明了上述问题具有归一化解。我们的贡献是，我们可以通过对规定规范约束的山口论证来处理超临界情况。
We are concerned with the following p-Laplacian equation $$\begin{aligned} -\varDelta _{p} u+|u|^{p-2}u=\mu u+|u|^{s-2}u,~\text {in}~{\mathbb {R}}^{N}, \end{aligned}$$where,,,,is the critical Sobolev exponent. Using constrained variational methods, we prove that the above problem has a normalized solution. Our contribution is that we can deal with the-supercritical caseby a mountain-pass argument on the prescribed-norm constraint.