度量图上非线性薛定谔方程峰值边界态的存在性和多重性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-06-07 DOI:10.1088/1361-6544/ad5133

Haixia Chen, Simone Dovetta, Angela Pistoia, Enrico Serra

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引用次数: 0

摘要

我们为一般紧凑和非紧凑度量图上的非线性薛定谔方程建立了单峰和多峰正约束状态的存在性和多重性。确切地说，我们构建了集中于每个奇数度大于或等于 3 的顶点的解。我们证明了这些解不是相关作用和能量函数的最小值。据我们所知，这是第一部展示集中在阶数大于 1 的顶点上的解的著作。证明基于合适的 Ljapunov-Schmidt 还原。

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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Existence and multiplicity of peaked bound states for nonlinear Schrödinger equations on metric graphs

We establish existence and multiplicity of one-peaked and multi-peaked positive bound states for nonlinear Schrödinger equations on general compact and noncompact metric graphs. Precisely, we construct solutions concentrating at every vertex of odd degree greater than or equal to 3. We show that these solutions are not minimizers of the associated action and energy functionals. To the best of our knowledge, this is the first work exhibiting solutions concentrating at vertices with degree different than 1. The proof is based on a suitable Ljapunov–Schmidt reduction.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.