具有临界项的分数阶薛定谔-泊松系统的解

doi:10.6040/j.issn.1671-9352.0.2020.713

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 56-63.doi: 10.6040/j.issn.1671-9352.0.2020.713

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具有临界项的分数阶薛定谔-泊松系统的解

郭凯利,冯晓晶^*

山西大学数学科学学院, 山西太原 030006

发布日期:2021-06-03
作者简介:郭凯利(1999— ),女,硕士研究生,研究方向为非线性泛函分析. E-mail:201922201003@email.sxu.edu.cn*通信作者简介:冯晓晶(1981— ),男,博士,副教授,研究方向为非线性泛函分析和偏微分方程. E-mail:fengxj@sxu.edu.cn
基金资助:
国家自然科学基金资助项目(12026218,12071266);山西省自然科学基金资助项目(201801D121002)

Solution to the fractional Schrödinger-Poisson systems with critical term

GUO Kai-li, FENG Xiao-jing^*

School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China

Published:2021-06-03

摘要/Abstract

摘要： 研究了一类带有临界项的分数阶薛定谔-泊松系统,这类系统广泛地应用于优化、金融、反应扩散等领域。由于系统中的薛定谔方程具有双临界项,因此困难之处在于估计山路临界值,且位势函数既不是周期的也不是渐近周期的,故不能运用通常的集中紧性原理,因此通过使用变分方法和改进的集中紧性原理,得到了该系统非平凡解的存在性。补充和推广了以往分数阶薛定谔-泊松系统的相关结果。

关键词: 分数阶薛定谔-泊松系统, 非平凡解, 临界指数

Abstract: This paper studies a class of fractional Schrödinger-Poisson systems with critical term, which has recently been widely used in optimization, finance, reaction diffusion and so on. Since the problem in the system has two critical terms, it is difficult to estimate the critical value of mountain pass; and the potential function is neither periodic nor asymptotic periodic, the usual concentration-compactness method is invalid. So we employ variational method and modified concentration-compactness principle to obtain the existence of nontrivial solution of this system. This result supplements and expands on the previous results on fractional Schrödinger-Poisson systems.

Key words: fractional Schrö, dinger-Poisson system, nontrivial solution, critical exponent

中图分类号:

O175.25

郭凯利,冯晓晶. 具有临界项的分数阶薛定谔-泊松系统的解[J]. 《山东大学学报(理学版)》, 2021, 56(6): 56-63.

GUO Kai-li, FENG Xiao-jing. Solution to the fractional Schrödinger-Poisson systems with critical term[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(6): 56-63.

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具有临界项的分数阶薛定谔-泊松系统的解

Solution to the fractional Schrödinger-Poisson systems with critical term

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