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Infinitely many solutions and concentration of ground state solutions for the Klein-Gordon-Maxwell system
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-24 , DOI: 10.1016/j.jmaa.2021.125521
Xiao-Qi Liu 1 , Chun-Lei Tang 1
Affiliation  

In this paper, we consider a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field, namely, the following Klein-Gordon-Maxwell system{Δu+(m2ω2)u(2ω+ϕ)ϕu=f(u),inR3,Δϕ=(ω+ϕ)u2,inR3, where 0<ω<m are constants and the nonlinearity f satisfies the superlinear condition. Here m and ω denote the mass and the phase respectively, while u and ϕ are unknowns. By using variational methods and some technique related to Pohozǎev identity, we construct bounded Palais-Smale sequences to obtain the existence of infinitely many high energy radial solutions. Moreover, we show that the ground state solutions of the Klein-Gordon-Maxwell system tend to the ground state solutions of the classical Schrödinger equation as ω0.



中文翻译:

Klein-Gordon-Maxwell 系统的无穷多解和基态解的浓度

在本文中,我们考虑描述与电磁场相互作用的非线性 Klein-Gordon 方程的孤立波的模型,即以下 Klein-Gordon-Maxwell 系统{-Δ+(2-ω2)-(2ω+φ)φ=F(),电阻3,-Δφ=-(ω+φ)2,电阻3, 在哪里 0<ω<是常数,非线性f满足超线性条件。这里mω分别表示质量和相位,而uϕ是未知数。通过使用变分方法和与 Pohozǎev 恒等式相关的一些技术,我们构造了有界 Palais-Smale 序列以获得无限多个高能径向解的存在性。此外,我们表明 Klein-Gordon-Maxwell 系统的基态解倾向于经典薛定谔方程的基态解为ω0.

更新日期:2021-08-03
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