一类拟线性薛定谔方程的多解性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 93-100.

一类拟线性薛定谔方程的多解性

薛艳昉^*(),朱新才()

信阳师范学院数学与统计学院河南信阳 464000

收稿日期:2021-05-13 修回日期:2022-07-25 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: ^*薛艳昉, E-mail: xueyanfang2015@163.com
作者简介:朱新才, E-mail: zhuxc68@163.com
基金资助:
国家自然科学基金(11901499);国家自然科学基金(11901500);信阳师范学院南湖学者青年项目(201912)

Existence of Multiple Solutions for a Class of Quasilinear Schrödinger Equations

Xue Yanfang^*(),Zhu Xincai()

College of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000

Received:2021-05-13 Revised:2022-07-25 Online:2023-02-26 Published:2023-03-07
Supported by:
The NSFC(11901499);The NSFC(11901500);Nanhu Scholar Program for Young Scholars of XYNU(201912)

摘要/Abstract

摘要：

该文研究了强制位势下拟线性薛定谔方程的多解性问题. 首先利用变量代换, 将拟线性方程转化成半线性方程, 然后借助喷泉定理, 得到了该方程的无穷多个高能量解.

关键词: 拟线性薛定谔方程, 喷泉定理, 强制位势

Abstract:

The multiple solutions are studied for a class of Quasilinear Schr?dinger equation under the coercive potential. By using the method of variable substitution, the quasilinear problem is transformed into a semilinear one, then infinitely many high energy solutions of the equation are obtained with the help of the fountain theorem.

Key words: Quasilinear Schr?dinger equations, Fountain theorem, Coercive potential

中图分类号:

O177.91

薛艳昉, 朱新才. 一类拟线性薛定谔方程的多解性[J]. 数学物理学报, 2023, 43(1): 93-100.

Xue Yanfang, Zhu Xincai. Existence of Multiple Solutions for a Class of Quasilinear Schrödinger Equations[J]. Acta mathematica scientia,Series A, 2023, 43(1): 93-100.

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