Electron. J. Differential Equations, Vol. 2024 (2024), No. 18, pp. 1-11.

Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

Lixia Wang, Pingping Zhao, Dong Zhang

Abstract:
In this article, we study the system of Klein-Gordon and Born-Infeld equations −Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u),x∈R3,Δϕ+βΔ4ϕ=4π(ω+ϕ)u2,x∈R3, where Δ4ϕ=div(|∇ϕ|2∇ϕ), ω is a positive constant. Assuming that the primitive of f(x,u) is of 2-superlinear growth in u at infinity, we prove the existence of multiple solutions using the fountain theorem. Here the potential V are allowed to be a sign-changing function.

Submitted October 30, 2023. Published February 16, 2024.
Math Subject Classifications: 35B33, 35J65, 35Q55.
Key Words: Klein-Gordon equation; Born-Infeld theory; superlinear; fountain theorem.
DOI: 10.58997/ejde.2024.18

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Lixia Wang
School of Sciences
Tianjin Chengjian University
Tianjin 300384, China
email: wanglixia0311@126.com
  Pingping Zhao
School of Sciences
Tianjin Chengjian University
Tianjin 300384, China
email: ppzhao_math@126.com
Dong Zhang
School of Sciences
Tianjin Chengjian University
Tianjin 300384, China
email: zhangdongtg@126.com

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