We consider the following equation

$$\begin{aligned} -\Delta u+u=Q_n(x)|u|^{p-2}u, \quad x\in {\mathbb {R}}^{N}, \end{aligned}$$

where \(Q_n\) are concrete bounded functions whose self-focusing core \(\text{ supp }\, Q_n^+\) shrinks to a finite set of points as \(n\rightarrow \infty \). We investigate the limiting profile of concentration for the ground state solutions and construct localized bound state solutions of concentration type.

中文翻译：

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自聚焦核不断缩小的Schrödinger方程解的极限轮廓

我们考虑以下等式

$$ \ begin {aligned}-\ Delta u + u = Q_n（x）| u | ^ {p-2} u，\ quad x \ in {\ mathbb {R}} ^ {N}，\ end {aligned } $$

其中\（Q_n \）是具体的有界函数，其自聚焦核心\（\ text {supp} \，Q_n ^ + \）缩小为一组有限的点，作为\（n \ rightarrow \ infty \）。我们研究了基态溶液浓度的极限分布，并构建了浓度类型的局部束缚态溶液。