Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case
Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case
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DOI：
10.1016/j.jfa.2020.108610
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发表时间：
2018-11
影响因子：
1.7
通讯作者：
N. Soave
中科院分区：
文献类型：
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作者：
N. Soave
在Sobolev临界情况下，研究了具有组合幂非线性- Δ u= λ u+ μ| u| q - 2 u+| u| 2 - 2 u的非线性Schrödinger方程基态的存在性和性质，该方程在N， N≥3，规定质量∫R N| u| 2= a 2。对于l2 -超临界微扰μ b|q - 2u的l2 -亚临界，l2 -临界，我们证明了几个存在/不存在和稳定性/不稳定性的结果。本研究可以看作是在归一化解背景下的Brezis-Nirenberg问题的对应，并且似乎是关于Sobolev临界NLSE在整个空间rn中存在归一化基态的第一个贡献。
We study existence and properties of ground states for the nonlinear Schrödinger equation with combined power nonlinearities− Δ u= λ u+ μ| u| q− 2 u+| u| 2⁎− 2 u in R N, N≥ 3, having prescribed mass∫ R N| u| 2= a 2, in the Sobolev critical case. For a L 2-subcritical, L 2-critical, of L 2-supercritical perturbation μ| u| q− 2 u we prove several existence/non-existence and stability/instability results. This study can be considered as a counterpart of the Brezis-Nirenberg problem in the context of normalized solutions, and seems to be the first contribution regarding existence of normalized ground states for the Sobolev critical NLSE in the whole space R N.