Existence and multiplicity of stationary solutions for a class of Maxwell–Dirac system. (November 2015)

• Record Type: Journal Article
• Authors: Zhang, Jian; Tang, Xianhua; Zhang, Wen
• Is Part Of: Nonlinear analysis. Volume 127(2015)
• Page Start: 298
• Page End: 311
• Publication Date: 2015-11
• Subjects: Maxwell–Dirac system -- Stationary solutions -- Asymptotically quadratic -- Strongly indefinite functionals; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.07.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with the following Maxwell–Dirac system { − i ∑ k = 1 3 α k ∂ k u + a β u + M ( x ) u − K ( x ) ϕ u = F u ( x, u ), − Δ ϕ = 4 π K ( x ) ∣ u ∣ 2, in R 3 where M ( x ) is a external potential and F ( x, u ) is an asymptotically quadratic nonlinearity modeling various types of interactions. In view of the effects of the nonlocal term, we use some special techniques to deal with the nonlocal term. Moreover, existence and multiplicity of stationary solutions are obtained for system without any periodicity assumption via variational methods.