一类相对非线性薛定谔方程解的存在性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 95-104.

一类相对非线性薛定谔方程解的存在性

邱雯^1,²,张贻民^1,^2,*(),AbdelgadirAhmed Adam³

¹ 武汉理工大学数学科学研究中心武汉 430070
² 武汉理工大学理学院数学系武汉 430070
³ Department of Mathematics, Taibah University Madinah Munawwarah, Saudi Arabia

收稿日期:2017-12-27 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 张贻民 E-mail:loiolo@qq.com; zhangym802@126.com; ahmedguangzhou17@gmail.com
基金资助:
国家自然科学基金(11471330);国家自然科学基金国家自然科学基金(11501555);国家自然科学基金(11771127);中央高校基本科研业务费专项基金(2017IVA-075);中央高校基本科研业务费专项基金(2017IVA076);中央高校基本科研业务费专项基金(2018-zy-138);中央高校基本科研业务费专项基金(2018IB014)

Existence of Nontrivial Solutions for a Class of Relativistic Nonlinear Schrödinger Equations

Wen Qiu^1,²,Yimin Zhang^1,^2,*(),Ahmed Adam Abdelgadir³

¹ Center of Mathematical Sciences, Wuhan University of Technology, Wuhan 430070
² Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070
³ Department of Mathematics, Taibah University Madinah Munawwarah, Saudi Arabia

Received:2017-12-27 Online:2019-02-26 Published:2019-03-12
Contact: Yimin Zhang E-mail:loiolo@qq.com; zhangym802@126.com; ahmedguangzhou17@gmail.com
Supported by:
the NSFC(11471330);the NSFC(11501555);the NSFC(11771127);the Fundamental Research Funds for the Central Universities(2017IVA-075);the Fundamental Research Funds for the Central Universities(2017IVA076);the Fundamental Research Funds for the Central Universities(2018-zy-138);the Fundamental Research Funds for the Central Universities(2018IB014)

摘要/Abstract

摘要：

利用临界点理论考虑了一类相对非线性薛定谔方程，主要通过变量代换将相对非线性薛定谔方程转化成半线性椭圆型方程.首先考虑位势函数为零时，将经典的场方程结果推广到了相对非线性薛定谔方程；而后利用临界点理论得到了有界位势情形方程非平凡解的存在性，在此情形，改进了文献[12-13]中的超线性条件.

关键词: 山路引理, 相对非线性薛定谔方程, 集中紧引理

Abstract:

Using the critical point theory, we consider a class of relativistic nonlinear Schrödinger equations. By introducing a change, we transform the relativistic nonlinear Schrödinger equations into the semilinear elliptic equations. First, we extend results of the classical field equation to the relativistic nonlinear Schrödinger equation. Then, the variational methods was used to obtain the existence of nontrivial solutions of the relativistic nonlinear Schrödinger equations with bounded potential. Moreover, we improved the general superlinear conditions which was used in [12-13].

Key words: Mountain pass theorem, Relativistic nonlinear Schrödinger equation, Concentration compactness principle

中图分类号:

O175.25

邱雯,张贻民,AbdelgadirAhmed Adam. 一类相对非线性薛定谔方程解的存在性[J]. 数学物理学报, 2019, 39(1): 95-104.

Wen Qiu,Yimin Zhang,Ahmed Adam Abdelgadir. Existence of Nontrivial Solutions for a Class of Relativistic Nonlinear Schrödinger Equations[J]. Acta mathematica scientia,Series A, 2019, 39(1): 95-104.

参考文献

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