arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2002.08344math.AP
收藏

具有至少质量临界增长的非线性薛定谔方程的归一化基态

Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth

Bartosz Bieganowski, Jarosław Mederski

备注：
to appear in Journal of Functional Analysis
发表信息：
J. Funct. Anal., Vol. 280, Issue 11 (2021), 108989
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们提出了一个简单的最小化方法，以显示存在的最小能量的解决方案，规范化的问题\begin{cases} -Δu + λu = g(u) \quad \mathrm{in} \ \mathbb{R}^N, \ N \geq 3, \\ u \in H^1(\mathbb{R}^N), \\ \int_{\mathbb{R}^N} |u|^2 \, dx = ρ> 0, \end{cases}，其中$ρ$规定和$(λ, u) \in \mathbb{R} \times H^1 (\mathbb{R}^N)$是要确定的。新方法的基础上直接最小化的能量泛函的线性组合的Nehari和Pohozaev约束的证明，它允许提供一般的增长假设施加在$g$。我们涵盖了最知名的物理例子和非线性增长的文献中考虑到目前为止，以及我们承认在$0$的质量临界增长。

英文摘要：

We propose a simple minimization method to show the existence of least energy solutions to the normalized problem \begin{cases} -Δu + λu = g(u) \quad \mathrm{in} \ \mathbb{R}^N, \ N \geq 3, \\ u \in H^1(\mathbb{R}^N), \\ \int_{\mathbb{R}^N} |u|^2 \, dx = ρ> 0, \end{cases} where $ρ$ is prescribed and $(λ, u) \in \mathbb{R} \times H^1 (\mathbb{R}^N)$ is to be determined. The new approach based on the direct minimization of the energy functional on the linear combination of Nehari and Pohozaev constraints is demonstrated, which allows to provide general growth assumptions imposed on $g$. We cover the most known physical examples and nonlinearities with growth considered in the literature so far as well as we admit the mass critical growth at $0$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑