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Existence and Multiplicity of Sign-Changing Solutions for Klein–Gordon Equation Coupled with Born–Infeld Theory with Subcritical Exponent

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Abstract

In this paper we consider the following Klein–Gordon equation coupled with Born–Infeld theory

$$\begin{aligned} \left\{ \begin{array}{ll} -{\Delta }u+[m^2-({\omega }+{\phi })^2]u=|u|^{p-2}u \quad &{}\text{ in }\ {\mathbb {R}}^3, \\ {\Delta }{\phi }+{\beta }{\Delta _4}{\phi }=4{\pi }({\omega +\phi })u^{2} &{}\text{ in }\ {\mathbb {R}}^3, \\ \end{array} \right. \end{aligned}$$

where \(2<p<6\), \(\omega >0\), \(\beta >0\) and m is a real constant. Assuming that \(0<\omega <\sqrt{\frac{p}{2}-1}|m|\) and \(2<p<4\) or \(0<{\omega }<|m|\) and \(4\le p <6\), we obtain the existence and multiplicity of sign-changing solutions via the method of invariant sets of descending flow.

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  1. School of Mathematical Sciences, TianGong University, Tianjin, 300387, People’s Republic of China

    Ziheng Zhang & Jianlun Liu

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  1. Ziheng Zhang
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Zhang, Z., Liu, J. Existence and Multiplicity of Sign-Changing Solutions for Klein–Gordon Equation Coupled with Born–Infeld Theory with Subcritical Exponent. Qual. Theory Dyn. Syst. 22, 7 (2023). https://doi.org/10.1007/s12346-022-00709-4

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