一般拟线性薛定谔方程正解的存在性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (4): 687-696.

一般拟线性薛定谔方程正解的存在性

谢朝东¹, 陈志辉²

1 贵州民族大学商学院贵阳 550025;
2 华南理工大学数学学院广州 510640

收稿日期:2017-04-14 修回日期:2017-11-15 出版日期:2018-08-26 发布日期:2018-08-26
通讯作者: 谢朝东,E-mail:xcd@gzmu.edu.cn E-mail:xcd@gzmu.edu.cn
作者简介:陈志辉,E-mail:mazhchen@scut.edu.cn
基金资助:
国家自然科学基金（11371146）和中国贵州省科学技术基金（黔科合J字LKM[2012]19）

On the Existence of Positive Solutions for Generalized Quasilinear Schrödinger Equations

Xie Chaodong¹, Chen Zhihui²

1 School of Economics & Management, Guizhou University for Ethinic Minorities, Guiyang 550025;
2 School of Mathematics, South China University of Technology, Guangzhou 510640

Received:2017-04-14 Revised:2017-11-15 Online:2018-08-26 Published:2018-08-26
Supported by:
Supported by the NSFC (11371146) and the Science and Technology Foundation of Guizhou Province of China under Grant Qiankehe-J-LKM[2012]19

摘要/Abstract

摘要： 通过对高阶项-div（g²（u）▽u）中g（u）的细致分析，该文证明了一类一般拟线性薛定谔方程正解的存在性.

关键词: 薛定谔方程, 山路定理, 临界点

Abstract: In this paper, we prove the existence of positive solutions for generalized quasilinear Schrödinger equations. By detailed analysis of g(u) in -div(g²(u)▽u), we have better results.

Key words: Schrödinger equations, Mountain Pass Theorem, Critical points

中图分类号:

O175.25

谢朝东, 陈志辉. 一般拟线性薛定谔方程正解的存在性[J]. 数学物理学报, 2018, 38(4): 687-696.

Xie Chaodong, Chen Zhihui. On the Existence of Positive Solutions for Generalized Quasilinear Schrödinger Equations[J]. Acta mathematica scientia,Series A, 2018, 38(4): 687-696.

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