标题： 关于薛定谔方程归一化解的存在性 显示英文标题

标题： On the existence of normalized solutions to Schrödinger equations

摘要： 我们研究了非线性薛定谔方程$$-\Delta v+V(x)v+\lambda v=v^{p} \text{ in } \mathbb R^N$$正解的存在性，该解具有指定质量$$\int_{\mathbb R^N} v^2=\mu,$$，并且集中在势能$V$的非退化临界点上，当指定质量$\mu$分别较大（当$p<1+\frac 4N$时）、较小（当$p>1+\frac 4N$时）或接近某个临界阈值（当$p=1+\frac 4N$时）。 显示英文摘要

摘要： We study the existence of positive solutions to the nonlinear Schr\"odinger equation $$-\Delta v+V(x)v+\lambda v=v^{p} \text{ in } \mathbb R^N$$ with a prescribed mass $$\int_{\mathbb R^N} v^2=\mu,$$ which concentrate at non-degenerate critical points of the potential $V$ as the prescribed mass $\mu$ is either large (when $p<1+\frac 4N$) or small (when $p>1+\frac 4N$) or it approaches some critical threshold (when $p=1+\frac 4N$).