Multiple positive solutions for nonhomogeneous Klein–Gordon–Maxwell equations

Hongxia Shi and Haibo Chen

Applied Mathematics and Computation, 2018, vol. 337, issue C, 504-513

Abstract: In this paper, we study the multiplicity of positive solutions for a class of nonhomogeneous Klein-Gordon-Maxwell equations {−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+h(x),inR3,Δϕ=(ω+ϕ)u2,inR3,where ω is a positive constant. Under some suitable assumptions on V(x), f(x, u) and h(x), we prove the existence of two positive solutions by using the Ekeland’s variational principle and the Mountain Pass Theorem. These results improve the related ones in the literature.

Keywords: Klein–Gordon–Maxwell equations; Variational methods; Cut-off functional; Pohozaev type identity (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:504-513

DOI: 10.1016/j.amc.2018.05.052

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