带电势的线性和非线性耦合 Choquard 系统的归一化解

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-04-15 DOI:10.1007/s43034-024-00348-7

Zhenyu Guo, Wenyan Jin

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引用次数: 0

摘要

在本文中，我们研究了在\(L^2\)约束下具有不同势的线性和非线性耦合的Choquard系统。我们利用埃克兰德变分原理证明了在\(L^2\)-次临界情况下，当维度大于或等于 2 时，该系统在不带电势的情况下有一个归一化的径向对称解。此外，在一些适当的假设条件下，还得到了一个有电位的具有规定（L^2）约束的正解。证明基于精炼的能量估计。

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Normalized solutions of linear and nonlinear coupled Choquard systems with potentials

In this paper, we study Choquard systems with linear and nonlinear couplings with different potentials under the \(L^2\)-constraint. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for \(L^2\)-subcritical case when the dimension is greater than or equal to 2 without potentials. In addition, a positive solution with prescribed \(L^2\)-constraint under some appropriate assumptions with the potentials was obtained. The proof is based on the refined energy estimates.

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.