Properties of solutions to semilinear elliptic problem with Hardy potential
Properties of solutions to semilinear elliptic problem with Hardy potential
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DOI：
10.1016/j.jde.2020.01.009
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发表时间：
2020-07
影响因子：
2.4
通讯作者：
J. Chern;Masato Hashizume;Gyeongha Hwang
中科院分区：
文献类型：
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作者：
J. Chern;Masato Hashizume;Gyeongha Hwang
我们考虑下面的非线性Neumann问题{-Δ u-γ u| X| 2+ μ u=| u| 2 s − 2 u| X| s in B R <$R N，N≥ 3 <$u <$v = 0 on <$B R其中γ< γ <$：=（N− 2）2 4，0< s< 2，2 s <$= 2（N− s）N− 2 B R是以原点为中心、半径为R的球。首先，我们建立了无穷多个在原点奇异的正径向解的存在性。其次，我们研究了最小能量解的存在性和正则性。最后，我们研究了正则最小能量解的对称性。
We consider the following nonlinear Neumann problem {− Δ u− γ u| x| 2+ μ u=| u| 2 s⁎− 2 u| x| s in B R⊂ R N, N≥ 3∂ u∂ ν= 0 on∂ B R where γ< γ‾:=(N− 2) 2 4, 0< s< 2, 2 s⁎= 2 (N− s) N− 2 and B R is the ball centered at the origin with radius R. Firstly, we establish the existence of infinitely many positive radial solutions which are singular at the origin. Secondly, we investigate the existence and regularity of a least-energy solution. Lastly, we study the symmetric properties of a regular least-energy solution.