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Multiple Solutions for the Klein-Gordon-Maxwell System with Steep Potential Well

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Abstract

In this paper, we concern the Klein-Gordon-Maxwell system with steep potential well

$$\left\{{\matrix{{- {\rm{\Delta u +}}\left({\lambda a\left(x \right) + 1} \right)u - \left({2\omega + \phi} \right)\phi u = f\left({x,u} \right),} \hfill & {{\rm{in}}\,{\mathbb{R}^3},} \hfill \cr {- {\rm{\Delta}}\phi {\rm{=}} - \left({\omega + \phi} \right){u^2},} \hfill & {{\rm{in}}\,{\mathbb{R}^3}.} \hfill \cr}} \right.$$

Without global and local compactness, we can tell the difference of multiple solutions from their norms in LP(ℝ3).

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Acknowledgments

The authors are very grateful to the referee and the handling editor for valuable suggestions, which helped us to improve our manuscript greatly.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Xiao-qi Liu & Chun-lei Tang

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  1. Xiao-qi Liu
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  2. Chun-lei Tang
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Correspondence to Chun-lei Tang.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos.11971393 and 11801465), by the China Postdoctoral Science Foundation (No.2020M683251) and by the Graduate Student Scientific Research Innovation Projects in Chongqing (No. CYB18116).

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Liu, Xq., Tang, Cl. Multiple Solutions for the Klein-Gordon-Maxwell System with Steep Potential Well. Acta Math. Appl. Sin. Engl. Ser. 37, 155–165 (2021). https://doi.org/10.1007/s10255-021-0986-z

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