具有L2约束的Schrödinger-Newton系统多峰解的不存在性

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI:10.1007/s10255-023-1086-z

Qing Guo, Li-xiu Duan

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引用次数: 0

摘要

本文研究了具有L2约束的薛定谔-牛顿系统。确切地说，我们证明了在V（x）及其一阶导数在这些点附近的渐近行为的某些假设下，不存在集中在V（x）的k个不同临界点的多峰归一化解。特别地，本文中V（x）的临界点必须是退化的。主要工具是局部Pohozaev类型的身份和爆炸分析。我们的结果还表明，Schrödinger-Newton问题的集中点的渐近行为与经典的Schrüdinger方程有很大的不同，这主要是由非局部项引起的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Non-existence of Multi-peak Solutions to the Schrödinger-Newton System with L2-constraint

In this paper, we are concerned with the the Schrödinger-Newton system with L²-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V(x) under certain assumptions on asymptotic behavior of V(x) and its first derivatives near these points. Especially, the critical points of V(x) in this paper must be degenerate.

The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.