数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 69-81.

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渐近线性Dirac方程的相对Morse指标及其多解性

单远()   

  1. 南京审计大学数学学院 南京 211815
  • 收稿日期:2021-01-13 修回日期:2022-09-22 出版日期:2023-02-26 发布日期:2023-03-07
  • 作者简介:单远, E-mail: shannjnu@gmail.com
  • 基金资助:
    国家自然科学基金(11701285);江苏省自然科学基金(BK20161053)

Relative Morse Index and Multiple Solutions for Asymptotically Linear Dirac Equation

Shan Yuan()   

  1. School of Mathematics, Nanjing Audit University, Nanjing 211815
  • Received:2021-01-13 Revised:2022-09-22 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    The NSFC(11701285);National Science Foundation of Jiangsu Province(BK20161053)

摘要:

该文主要研究Dirac方程周期解的存在性和多重性. 通过引入相对Morse指标对相应的线性Dirac方程进行分类, 并给出解存在的扭转性条件.

关键词: 相对Morse指标, Dirac方程的周期解, 扭转性条件

Abstract:

This paper is concerned with the existence and multiplicity of periodic solutions for Dirac equation. We will establish a relative Morse index theory to classify the associated linear Dirac equation. Under a general twist condition for the nonlinear part via the relative Morse index, existence of multiple solutions are obtained.

Key words: Relative Morse index, Periodic solution of Dirac equation, Twist condition

中图分类号: 

  • O177.91