Lixia Wang, Pingping Zhao, Dong Zhang
Abstract:
In this article, we study the system of Klein-Gordon and Born-Infeld 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 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.2023.18
Show me the PDF file (338 KB), TEX file for this article.
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Lixia Wang School of Sciences Tianjin Chengjian University Tianjin 300384, China email: wanglixia0311@126.com |
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| Pingping Zhao School of Sciences Tianjin Chengjian University Tianjin 300384, China email: ppzhao_math@126.com | |
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Dong Zhang School of Sciences Tianjin Chengjian University Tianjin 300384, China email: zhangdongtg@126.com |
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