Normalized solutions for Chern–Simons–Schrödinger system with mixed dispersion and critical exponential growth

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-08-04 DOI:10.1002/mma.10383

Chenlu Wei, Lixi Wen

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Abstract

This paper focuses on the existence of normalized solutions for the Chern–Simons–Schrödinger system with mixed dispersion and critical exponential growth. These solutions correspond to critical points of the underlying energy functional under the $L^{2}$ -norm constraint, namely, $\int_{ℝ^{2}} u^{2} d x = c > 0$ . Under certain mild assumptions, we establish the existence of nontrivial solutions by developing new mathematical strategies and analytical techniques for the given system. These results extend and improve the results in the existing literature.

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具有混合分散和临界指数增长的切尔诺-西蒙斯-薛定谔系统的归一化解法

本文主要研究具有混合分散和临界指数增长的切尔-西蒙斯-薛定谔系统的归一化解的存在性。这些解对应于-规范约束下基本能量函数的临界点，即。在某些温和的假设条件下，我们通过为给定系统开发新的数学策略和分析技术，建立了非微观解的存在性。这些结果扩展并改进了现有文献中的结果。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.

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