Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1013-1023.

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Multiple Periodic Solutions for a Class of Stationary Dirac Equations with Local Nonlinearity

Qingye Zhang1,*(),Bin Xu2()   

  1. 1 School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
    2 School of Mathematics and Statistics, Jiangsu Normal University, Jiangsu Xuzhou 221116
  • Received:2020-09-17 Online:2021-08-26 Published:2021-08-09
  • Contact: Qingye Zhang;
  • Supported by:
    the NSFC(11761036);the NSFC(11201196);the NSF of Jiangxi Province(20171BAB211002)


In this paper, we mainly study multiple periodic solutions for a class of stationary Dirac equations with local nonlinearity via variational methods. Under some fairly mild conditions on the nonlinearity, we show that the existence of a sequence of nontrivial periodic solutions is rather a local phenomenon, which is only forced by the sublinearity of the nonlinearity near the origin. Meanwhile, some recent results from the literature are generalized and essentially improved.

Key words: Dirac equation, Periodic solution, Variational method, Local nonlinearity

CLC Number: 

  • O175