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Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jfa.2020.108610 Nicola Soave
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jfa.2020.108610 Nicola Soave
We study existence and properties of ground states for the nonlinear Schrodinger equation with combined power nonlinearities \[ -\Delta u= \lambda u + \mu |u|^{q-2} u + |u|^{p-2} u \qquad \text{in $\mathbb{R}^N$, $N \ge 1$,} \] having prescribed mass \[ \int_{\mathbb{R}^N} |u|^2 = a^2. \] Under different assumptions on $q 0$ and $\mu \in \mathbb{R}$ we prove several existence and stability/instability results. In particular, we consider cases when \[ 2
更新日期：2020-10-01
中文翻译：
具有组合非线性的 NLS 方程的归一化基态：Sobolev 临界情况
我们研究具有组合功率非线性的非线性薛定谔方程的基态的存在性和性质 \[ -\Delta u= \lambda u + \mu |u|^{q-2} u + |u|^{p-2} u \qquad \text{in $\mathbb{R}^N$, $N \ge 1$,} \] 具有规定的质量 \[ \int_{\mathbb{R}^N} |u|^2 = a ^2。\] 在 $q 0$ 和 $\mu \in \mathbb{R}$ 的不同假设下，我们证明了几个存在性和稳定性/不稳定性结果。特别地，我们考虑 \[ 2
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