中文摘要：

该文研究如下Klein—Gordon—Maxwell系统， {-△Ф＋Фu^2=-ωu^2. x∈R^3,-△u＋u-（2ω＋Ф）Фu=a（x）｜u｜^p-2u＋λb（x）｜u｜^q-2u,x∈R^3多重解的存在性，其中4〈p〈6，1〈q〈2，λ〉0．在a（x）、b（x）、参数λ满足一定的假设条件下，通过变分方法证明了系统无穷解的存在性．补充和完善了以上方程解存在性的以往结果．

英文摘要：

In this paper, we establish the multiplicity of solutions for the Klein-Gordon- Maxwell system{-△Ф＋Фu^2=-ωu^2. x∈R^3,-△u＋u-（2ω＋Ф）Фu=a（x）｜u｜^p-2u＋λb（x）｜u｜^q-2u,x∈R^3 where 4 〈 p 〈 6, 1 〈 q 〈 2, A 〉 O. Under some assumptions on the a（x）, b（x）, λ, the multiplicity result of solutions for the system was obtained by variational methods. Our result is a complement to some recent works concerning the existence of solutions of the above equation.