A Pohozaev type identity and its application to uniqueness of positive radial solutions of Brezis-Nirenberg problem on an annulus
A Pohozaev type identity and its application to uniqueness of positive radial solutions of Brezis-Nirenberg problem on an annulus
复制标题
Pohozaev型恒等式及其在环面上Brezis-Nirenberg问题正径向解唯一性中的应用
DOI：
10.1016/j.jmaa.2020.124901
复制
发表时间：
2021
影响因子：
1.3
通讯作者：
KohtaroWatanabe
中科院分区：
文献类型：
--
作者：
Naoki Shioji;KohtaroWatanabe
研究了Brezis-Nirenberg问题{Δ u（x）+ λ u（x）+ u（x）p= 0，x∈ A a，B，u（x）= 0，x ∈ A a，B，其中n≥ 3，B> a> 0，0< λ< λ 1，p>（n+ 2）/（n-2），λ 1是− Δ的第一特征值，在A a，B={x∈ Rn| a<|X| < B}。特别地，在n= 3的情况下，我们完全解决了这个问题，没有任何额外的假设，并且在n≥ 4的情况下，我们证明了0< λ 1− λ <$1下的唯一性结果。这些结果是通过一种Pohožaev恒等式得到的。
We study the uniqueness of positive radial solutions of the Brezis-Nirenberg problem {Δ u (x)+ λ u (x)+ u (x) p= 0, x∈ A a, b, u (x)= 0, x∈∂ A a, b, where n≥ 3, b> a> 0, 0< λ< λ 1, p>(n+ 2)/(n− 2) and λ 1 is the first eigenvalue of− Δ under the Dirichlet boundary condition on A a, b={x∈ R n| a<| x|< b}. In particular, in the case n= 3, we completely solve the problem without any additional assumption, and in the case n≥ 4, we show the uniqueness result under 0< λ 1− λ≪ 1. These results are obtained through a kind of Pohožaev identity.