临界乔卡方程的多凸点解决方案

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI:10.1137/23m1581820

Jiankang Xia, Xu Zhang

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷，第 3 期，第 3832-3860 页，2024 年 6 月。摘要。我们关注临界乔夸德方程[math]，其中[math]、[math]是阶数为[math]的里兹势，指数[math]是关于哈代-利特尔伍德-索博列夫不等式的临界值。如果[math]势在其中一个变量中是周期性的，并且允许在最大点附近以较快的衰减速度出现全局最大值，那么通过结合变分胶合方法和惩罚技术，对于每一个[math]，我们证明了这个非局部方程存在无穷多个[math]凸点正解，在无穷处表现出多项式衰减。我们的结果证明了乔夸德方程的非局部特征，并且不依赖于正解的唯一性或非整定性，这与局部山边方程的结果截然不同。

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Multibump Solutions for Critical Choquard Equation

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3832-3860, June 2024.
Abstract. We are concerned with the critical Choquard equation [math] where [math], [math] is the Riesz potential with order [math], and the exponent [math] is critical with respect to the Hardy–Littlewood–Sobolev inequality. By combining the variational gluing method and a penalization technique, for every [math], we prove the existence of infinitely many [math]-bump positive solutions for this nonlocal equation exhibiting a polynomial decay at infinity if the potential [math] is periodic in one of its variables and permits a global maxima with a fast decay rate near the maximum point. Our results demonstrate the nonlocal features of the Choquard equation and do not depend on the uniqueness or nondegeneracy property of positive solutions, which is in contrast to the results of the local Yamabe equation.

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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.