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A Pohožaev type identity and its application to uniqueness of positive radial solutions of Brezis-Nirenberg problem on an annulus
Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.jmaa.2020.124901 Naoki Shioji , Kohtaro Watanabe
中文翻译:
Pohožaev型恒等式及其在环上Brezis-Nirenberg问题正径向解的唯一性中
更新日期:2021-01-07
Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.jmaa.2020.124901 Naoki Shioji , Kohtaro Watanabe
We study the uniqueness of positive radial solutions of the Brezis-Nirenberg problem where , , , and is the first eigenvalue of −Δ under the Dirichlet boundary condition on . In particular, in the case , we completely solve the problem without any additional assumption, and in the case , we show the uniqueness result under . These results are obtained through a kind of Pohožaev identity.
中文翻译:
Pohožaev型恒等式及其在环上Brezis-Nirenberg问题正径向解的唯一性中
我们研究Brezis-Nirenberg问题的正径向解的唯一性 哪里 , , , 和 是Dirichlet边界条件下-Δ的第一个特征值 。特别是,我们将完全解决问题,而无需任何其他假设,并且在这种情况下 ,我们在下显示唯一性结果 。这些结果是通过一种Pohožaev身份获得的。