Existence and multiplicity of stationary solutions for a class of Maxwell-Dirac system

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• 作者：Jian Zhang^a ; ^{zhangjian433130@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xianhua Tang^b ; ^{tangxh@mail.csu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Wen Zhang^b ; ^{zwmath2011@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Maxwell&ndash ; Dirac system ; Stationary solutions ; Asymptotically quadratic ; Strongly indefinite functionals
• 刊名：Nonlinear Analysis
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：127
• 期：Complete
• 页码：298-311
• 全文大小：683 K

文摘

This paper is concerned with the following Maxwell–Dirac system where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15002412&_mathId=si2.gif&_user=111111111&_pii=S0362546X15002412&_rdoc=1&_issn=0362546X&md5=ed83e0463a374f314f0f12672a7be0f6" title="Click to view the MathML source">M(x)class="mathContainer hidden">class="mathCode">$M\left(x\right)$ is a external potential and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15002412&_mathId=si3.gif&_user=111111111&_pii=S0362546X15002412&_rdoc=1&_issn=0362546X&md5=5bfc4241dbf658fd71c8454739370851" title="Click to view the MathML source">F(x,u)class="mathContainer hidden">class="mathCode">$F(x,u)$ 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.