非自治分式 HLS 下临界 Choquard 方程归一化解的存在性、多重性和渐近行为

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-09-13 DOI:10.1007/s13540-024-00338-5

Jianlun Liu, Hong-Rui Sun, Ziheng Zhang

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引用次数: 0

摘要

在本文中，我们研究了一类具有纯功率非线性扰动的非自治下临界分式乔夸特方程。在势函数 h 的一些合理假设下，我们证明了问题的基态解的存在并讨论了其渐近行为。同时，我们还证明了当\(\varepsilon \)足够小时，归一化解的数目至少是 h 的全局最大点的数目。

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, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation

In this paper, we study a class of non-autonomous lower critical fractional Choquard equation with a pure-power nonlinear perturbation. Under some reasonable assumptions on the potential function h, we prove the existence and discuss asymptotic behavior of ground state solutions for our problem. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximum points of h when \(\varepsilon \) is small enough.

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.