Electron. J. Differential Equations, Vol. 2024 (2024), No. 18, pp. 111.
Existence of high energy solutions for superlinear coupled KleinGordons
and BornInfeld equations
Lixia Wang, Pingping Zhao, Dong Zhang
Abstract:
In this article, we study the system of KleinGordon and BornInfeld equations
$$\displaylines{
\Delta u +V(x)u(2\omega+\phi)\phi u =f(x,u), \quad x\in R^3,\cr
\Delta \phi+\beta\Delta_4\phi=4\pi(\omega+\phi)u^2, \quad x\in R^3,
}$$
where \(\Delta_4\phi=\hbox{div}(\nabla\phi^2\nabla\phi)\),
\(\omega\) is a positive constant. Assuming that the primitive of
\(f(x,u)\) is of 2superlinear 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 signchanging function.
Submitted October 30, 2023. Published February 16, 2024.
Math Subject Classifications: 35B33, 35J65, 35Q55.
Key Words: KleinGordon equation; BornInfeld theory; superlinear; fountain theorem.
DOI: 10.58997/ejde.2023.18
Show me the PDF file (338 KB),
TEX file for this article.

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

Return to the EJDE web page