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Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system

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Abstract

In this paper, we consider the fractional subcritical Klein-Gordon-Maxwell system as follows:

$$\begin{aligned} \left\{ \begin{aligned}&(-\Delta )^{s} u+V(x)u-(2\omega +\phi (x) )\phi (x)u= f(x,u), \,\,\,&\text {in } \mathbb {R}^3, \\&(\Delta )^{s} \phi (x)=(\omega +\phi (x) )u^2, \,\,\,&\text {in } \mathbb {R}^3, \end{aligned} \right. \end{aligned}$$

the nonlinearity f is superlinear at infinity with subcritical growth and V is continuous and coercive. For the case when f is odd in u we obtain infinitely many high energy sign-changing solutions for the above problem by using a combination of invariant sets method and the Ljusternik-Schnirelman type minimax method.

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Acknowledgements

Li Wang was supported by the National Natural Science Foundation of China (Grant No. 12161038) and Science and Technology project of Jiangxi provincial Department of Education (Grant Nos. GJJ212204, GJJ2200635). Jijiang Sun was supported by the National Natural Science Foundation of China (Grant No. 11861046) and Jiangxi Provincial Natural Science Foundation (Grant No. 20212BAB201026)

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Authors and Affiliations

  1. College of Science, East China Jiaotong University, Nanchang, 330013, China

    Li Wang & Liqin Tang

  2. Department of Mathematics, Nanchang University, Nanchang, 330031, China

    Jijiang Sun

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  1. Li Wang
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  2. Liqin Tang
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Correspondence to Jijiang Sun.

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Wang, L., Tang, L. & Sun, J. Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system. Fract Calc Appl Anal 26, 672–693 (2023). https://doi.org/10.1007/s13540-023-00129-4

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  • DOI: https://doi.org/10.1007/s13540-023-00129-4

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