On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-06-03 DOI:10.1007/s13540-024-00296-y

Lin Li, Huo Tao, Stepan Tersian

引用次数: 0

Abstract

In this paper, we establish the existence of standing wave solutions for a class of nonlinear fractional Schrödinger-Poisson system involving nonlinearity with subcritical and critical growth. We suppose that the potential V satisfies either Palais-Smale type condition or there exists a bounded domain \(\varOmega \) such that V has no critical point in \(\partial \varOmega \). To overcome the “lack of compactness" of the problem, we combine Del Pino-Felmer’s penalization technique with Moser’s iteration method and some ideas from Alves [1].

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关于一类非线性分数薛定谔-泊松系统解的存在性：亚临界和临界情况

在本文中，我们建立了一类非线性分式薛定谔-泊松系统的驻波解的存在性，该系统涉及具有亚临界和临界增长的非线性。我们假设势 V 满足 Palais-Smale 类型条件，或者存在一个有界域 \(\varOmega \)，使得 V 在 \(\partial \varOmega \)中没有临界点。为了克服问题的 "不紧凑性"，我们将 Del Pino-Felmer 的惩罚技术与 Moser 的迭代法以及 Alves [1] 的一些观点结合起来。

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

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.