具有超临界捕获势的半线性Schrödinger方程的平稳解

IF 0.5 Q3 MATHEMATICS

Archivum Mathematicum Pub Date : 2022-10-25 DOI:10.5817/AM2023-1-31

F. Ficek

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引用次数: 0

摘要

非线性Schr\ odinger方程通常使用限于能量亚临界维的变分方法进行研究。本文提出了一种基于射击法的方法，可以证明临界和超临界情况下基态的存在性。我们在系统上提出了足以使这种方法起作用的假设。作为例子，我们考虑具有谐波势的Schr\ odinger-Newton方程和Gross-Pitaevskii方程。

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Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions

Nonlinear Schr\"odinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schr\"odinger-Newton and Gross-Pitaevskii equations with harmonic potentials.

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来源期刊

Archivum Mathematicum MATHEMATICS-

CiteScore

0.70

自引率

16.70%

发文量

审稿时长

35 weeks

期刊介绍： Archivum Mathematicum is a mathematical journal which publishes exclusively scientific mathematical papers. The journal, founded in 1965, is published by the Department of Mathematics and Statistics of the Faculty of Science of Masaryk University. A review of each published paper appears in Mathematical Reviews and also in Zentralblatt für Mathematik. The journal is indexed by Scopus.