一类带局部非线性项的静态狄拉克方程的多重周期解

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1013-1023.

一类带局部非线性项的静态狄拉克方程的多重周期解

张清业^1,*(),徐斌²()

¹ 江西师范大学数学与统计学院南昌 330022
² 江苏师范大学数学与统计学院江苏徐州 221116

收稿日期:2020-09-17 出版日期:2021-08-26 发布日期:2021-08-09
通讯作者: 张清业 E-mail:zhangqy@jxnu.edu.cn;dream-010@163.com
作者简介:徐斌, E-mail: dream-010@163.com
基金资助:
国家自然科学基金(11761036);国家自然科学基金(11201196);江西省自然科学基金(20171BAB211002)

Multiple Periodic Solutions for a Class of Stationary Dirac Equations with Local Nonlinearity

Qingye Zhang^1,*(),Bin Xu²()

¹ School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
² School of Mathematics and Statistics, Jiangsu Normal University, Jiangsu Xuzhou 221116

Received:2020-09-17 Online:2021-08-26 Published:2021-08-09
Contact: Qingye Zhang E-mail:zhangqy@jxnu.edu.cn;dream-010@163.com
Supported by:
the NSFC(11761036);the NSFC(11201196);the NSF of Jiangxi Province(20171BAB211002)

摘要/Abstract

摘要：

借助于变分方法，该文主要研究了一类带局部非线性项的静态狄拉克方程的多重周期解.在非线性项满足较为宽泛的条件的假设下，该文表明了这类方程一列非平凡周期解的存在性是一种局部现象，该现象仅由非线性项在原点附近的次线性所决定.与此同时，文献中最近的一些相关结果被推广并得到本质的改进.

关键词: 狄拉克方程, 周期解, 变分方法, 局部非线性

Abstract:

In this paper, we mainly study multiple periodic solutions for a class of stationary Dirac equations with local nonlinearity via variational methods. Under some fairly mild conditions on the nonlinearity, we show that the existence of a sequence of nontrivial periodic solutions is rather a local phenomenon, which is only forced by the sublinearity of the nonlinearity near the origin. Meanwhile, some recent results from the literature are generalized and essentially improved.

Key words: Dirac equation, Periodic solution, Variational method, Local nonlinearity

中图分类号:

O175

张清业,徐斌. 一类带局部非线性项的静态狄拉克方程的多重周期解[J]. 数学物理学报, 2021, 41(4): 1013-1023.

Qingye Zhang,Bin Xu. Multiple Periodic Solutions for a Class of Stationary Dirac Equations with Local Nonlinearity[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1013-1023.

参考文献 23

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