数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 417-428.

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一类带扰动项的拟线性薛定谔方程的多解性

陈铭超(),薛艳昉*()   

  1. 信阳师范大学数学与统计学院 河南信阳 464000
  • 收稿日期:2023-02-09 修回日期:2023-08-24 出版日期:2024-04-26 发布日期:2024-04-07
  • 通讯作者: * 薛艳昉,Email:xueyanfang2015@163.com
  • 作者简介:陈铭超,Email:1432064866@qq.com
  • 基金资助:
    国家自然科学基金(11901499);信阳师范学院南湖学者青年项目(201912)

Multiple Solutions for a Class of Quasilinear Schrödinger Equations with a Perturbed Term

Chen Mingchao(),Xue Yanfang*()   

  1. College of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000
  • Received:2023-02-09 Revised:2023-08-24 Online:2024-04-26 Published:2024-04-07
  • Supported by:
    NSFC(11901499);Nanhu Scholar Program for Young Scholars of XYNU(201912)

摘要:

该文研究了强制位势下非齐次拟线性薛定谔方程的多解性问题. 通过山路定理和 Ekeland 变分原理, 得到了该方程两个不同的解. 所得结论是对此类拟线性方程已有结果的补充和推广.

关键词: 拟线性薛定谔方程, 非齐次, 山路定理, Ekeland 变分原理

Abstract:

In this paper, we study the multiplicity of solutions for nonhomogeneous quasilinear Schrödinger equation with coercive potential. We obtain two different solutions by applying the Mountain Pass Theorem and Ekeland's Variational Principle. The results in this paper extend and complement previously known results to the quasilinear equations.

Key words: Quasilinear Schr?dinger equation, Nonhomogeneous, Mountain Pass Theorem, Ekeland's Variational Principle

中图分类号: 

  • O177.91