Standing Waves for Non-periodic Discrete Nonlinear Schrödinger Equations via Morse Theory

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-02 DOI:10.1007/s40840-024-01678-4

引用次数: 0

Abstract

In this paper, we consider the following discrete nonlinear Schrödinger equation $$\begin{aligned} \left\{ \begin{array}{l} -\Delta u_{n}+V_{n}u_{n}-\omega u_{n}=f_{n}(u_{n}), \quad n \in \mathbb {Z}, \\ \lim _{|n| \rightarrow \infty } u_{n}=0, \end{array}\right. \end{aligned}$$ with non-periodic potentials. We obtain the existence of nontrivial solutions of this equation with various nonlinearities by using Morse theory. In this way, we need to compute the critical groups of the corresponding action functional of the equation. To the best of our knowledge, there is no result focusing on this issue in the literature.

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通过莫尔斯理论研究非周期性离散非线性薛定谔方程的驻波

摘要在本文中，我们考虑以下离散非线性薛定谔方程 $$\begin{aligned}\left\{ \begin{array}{l} -\Delta u_{n}+V_{n}u_{n}-\omega u_{n}=f_{n}(u_{n}), \quad n \in \mathbb {Z}, \\\lim _{|n| \rightarrow \infty } u_{n}=0, \end{array}\right.\end{aligned}$$ 具有非周期性势。我们利用莫尔斯理论得到了这个方程的非线性解的存在性。这样，我们就需要计算方程相应作用函数的临界群。据我们所知，文献中还没有关注这一问题的结果。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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