Ground state solutions for Klein–Gordon–Maxwell system with steep potential well

2019 ◽  
Vol 90 ◽  
pp. 175-180 ◽  
Author(s):  
Xiao-Qi Liu ◽  
Shang-Jie Chen ◽  
Chun-Lei Tang
Keyword(s):  
Ground State ◽  
Potential Well ◽  
Maxwell System ◽  
Ground State Solutions ◽  
Klein Gordon ◽  
Steep Potential Well

scholarly journals Existence result for critical Klein-Gordon-Maxwell system involving steep potential well

2021 ◽  
Author(s):  
Canlin Gan
Keyword(s):  
Ground State ◽  
Existence Result ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
Potential Well ◽  
Maxwell System ◽  
Cerami Sequence ◽  
Klein Gordon ◽  
Steep Potential Well ◽  
Existing Result

This paper deals with the following system \begin{equation*} \left\{\begin{aligned} &{-\Delta u+ (\lambda A(x)+1)u-(2\omega+\phi) \phi u=\mu f(u)+u^{5}}, & & {\quad x \in \mathbb{R}^{3}}, \\ &{\Delta \phi=(\omega+\phi) u^{2}}, & & {\quad x \in \mathbb{R}^{3}}, \end{aligned}\right. \end{equation*} where $\lambda, \mu>0$ are positive parameters. Under some suitable conditions on $A$ and $f$, we show the boundedness of Cerami sequence for the above system by adopting Poho\v{z}aev identity and then prove the existence of ground state solution for the above system on Nehari manifold by using Br\’{e}zis-Nirenberg technique, which improve the existing result in the literature.

scholarly journals Positive ground state solutions for the critical Klein–Gordon–Maxwell system with potentials

2012 ◽  
Vol 75 (10) ◽  
pp. 4068-4078 ◽  
Author(s):  
Paulo C. Carrião ◽  
Patrícia L. Cunha ◽  
Olímpio H. Miyagaki
Keyword(s):  
Ground State ◽  
Maxwell System ◽  
Ground State Solutions ◽  
Klein Gordon
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