Multiple Normalized Solutions for First Order Hamiltonian Systems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI:10.1137/23m1584575

Yuxia Guo, Yuanyang Yu

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3861-3885, June 2024.
Abstract. In this paper, we study the following first order Hamiltonian systems: [math] where [math], [math], [math] arises as the Lagrange multiplier, and [math] are [math] real matrices with [math]. Using the multiplicity theorem of Ljusternik–Schnirelmann together with variational methods, we show the existence of multiple normalized homoclinic solutions for this problem. We deal with not only the case det[math] for all [math] in a set of nonzero measure, but also the case det[math] for all [math]. In particular, we also obtain bifurcation results of this problem.

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一阶哈密顿系统的多重归一化解法

SIAM 数学分析期刊》第 56 卷第 3 期第 3861-3885 页，2024 年 6 月。摘要本文研究下列一阶哈密顿系统：[其中[math]、[math]、[math]为拉格朗日乘数，[math]为带[math]的[math]实矩阵。］利用 Ljusternik-Schnirelmann 的多重性定理和变分法，我们证明了该问题存在多个归一化同线性解。我们不仅处理了非零度量集合中所有[math]的 det[math] 情况，还处理了所有[math]的 det[math] 情况。特别是，我们还得到了这个问题的分岔结果。

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

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.