论文标题
非线性schrödinger方程的归一化基态，至少质量临界增长
Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth
论文作者
论文摘要
我们提出了一种简单的最小化方法，以向归一化问题\ begin {case}展示最少能量解决方案的存在 -ΔU +λu= g（u）\ quad \ mathrm {in} \ \ \ \ \ \ \ \ \ \ {r}^n，\ n \ geq 3，\ \ u \ in H^1（\ MathBb {r} \ end {case}其中规定了$ρ$，并且要确定$（λ，u）\ in \ mathbb {r} \ times h^1（\ mathbb {r}^n）$。证明了基于能量功能在Nehari和Pohozaev约束的线性组合上的直接最小化的新方法，这允许提供对$ G $的一般增长假设。到目前为止，我们涵盖了文献中考虑的最著名的实例和非线性，同样我们承认质量临界增长率为$ 0 $。
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 $0$.
