On solutions for a class of Klein–Gordon equations coupled with Born–Infeld theory with Berestycki–Lions conditions on $ \mathbb{R}^3 $

Jiayi Fei; Qiongfen Zhang; Jiayi Fei; Qiongfen Zhang

doi:10.3934/era.2024108

Electronic Research Archive

2024, Volume 32, Issue 4: 2363-2379. doi: 10.3934/era.2024108

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On solutions for a class of Klein–Gordon equations coupled with Born–Infeld theory with Berestycki–Lions conditions on $ \mathbb{R}^3 $

Jiayi Fei ^1,2,
Qiongfen Zhang ^{1,2
,
,}

1.
School of Mathematics and Statistics, Guilin University of Technology, Guangxi 541004, China
2.
Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guangxi 541004, China

Received: 19 January 2024 Revised: 13 March 2024 Accepted: 17 March 2024 Published: 25 March 2024

In this paper, the existence of multiple solutions for a class of Klein–Gordon equations coupled with Born–Infeld theory was investigated. The potential and the primitive of the nonlinearity in this kind of elliptic equations are both allowed to be sign-changing. Besides, we assumed that the nonlinearity satisfies the Berestycki–Lions type conditions. By employing Ekeland's variational principle, mountain pass theorem, Pohožaev identity, and various other techniques, two nontrivial solutions were obtained under some suitable conditions.
- Klein–Gordon equation,
- Born–Infeld theory,
- nontrivial solutions,
- Berestycki-Lions conditions,
- cut-off function
Citation: Jiayi Fei, Qiongfen Zhang. On solutions for a class of Klein–Gordon equations coupled with Born–Infeld theory with Berestycki–Lions conditions on $ \mathbb{R}^3 $[J]. Electronic Research Archive, 2024, 32(4): 2363-2379. doi: 10.3934/era.2024108

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Abstract

In this paper, the existence of multiple solutions for a class of Klein–Gordon equations coupled with Born–Infeld theory was investigated. The potential and the primitive of the nonlinearity in this kind of elliptic equations are both allowed to be sign-changing. Besides, we assumed that the nonlinearity satisfies the Berestycki–Lions type conditions. By employing Ekeland's variational principle, mountain pass theorem, Pohožaev identity, and various other techniques, two nontrivial solutions were obtained under some suitable conditions.

References

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