Elsevier

Applied Mathematics Letters

Volume 91, May 2019, Pages 158-164
Applied Mathematics Letters

Improved results for Klein–Gorden–Maxwell systems with critical growth

https://doi.org/10.1016/j.aml.2018.12.015Get rights and content
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Abstract

In this paper we consider the following Klein–Gorden–Maxwell system Δu+V0u(2w+ϕ)ϕu=λ|u|p2u+|u|4u,xR3,Δϕ=(w+ϕ)u2,xR3,where λ, w and V0 are positive real constants. By employing some analytical skills and using the variational method, we prove some results about the existence of ground state solutions for the system under a general condition imposed on V0. Our results improve and extend some related ones in the literature.

Keywords

Klein–Gorden–Maxwell system
Variational method
Critical exponent
Ground state

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This work was supported by the National Natural Science Foundation of China (Nos. 11571370, 11801574, 11501190) and Central South University Innovation-Driven Project for Young Scholars (No. 2019CX022).