Periodic solutions to a nonlinear Dirac-Klein-Gordon system with concave and convex nonlinearities

Hua-Yang Wang; Yanheng Ding; Pan Chen

doi:10.3934/cpaa.2023046

Article Contents

2023, Volume 22, Issue 6: 1763-1782. Doi: 10.3934/cpaa.2023046

This issue Previous Article Symmetry and monotonicity of positive solutions to systems involving general pseudo-relativistic operators Next Article A nonlinear attraction-repulsion Keller–Segel model with double sublinear absorptions: criteria toward boundedness

Periodic solutions to a nonlinear Dirac-Klein-Gordon system with concave and convex nonlinearities

1.
Academy of Mathematics and System Science, Chinese Academy of Sciences, 100190 Beijing, China
2.
University of Chinese Academy of Sciences, 100049 Beijing, China

^*Corresponding author
^*Corresponding author

Received: August 2022

Revised: January 2023

Early access: March 22, 2023

Published online: March 22, 2023

The second author is supported by the National Key Research and Development Program of China (Grant No. 2022YFA1005600) and the National Natural Science Foundation of China (Grant No. 11871242, No. 12031015 and No. 12271508).

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Abstract

Using the variational method, we study the existence and multiplicity of periodic solutions to nonlinear Dirac-Klein-Gordon systems with two types of nonlinearities. Both the Dirac field and the Klein–Gordon field considered here are general nonlinear fields, different from previously considered models. Moreover, results for the regularity of the solutions are given. In addition, we obtain the soliton-like solution of Dirac-Klein-Gordon systems by approximation of periodic solutions.

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Mathematics Subject Classification: Primary: 35Q4035J50; Secondary: 49J35.

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