径向对称位势下Klein-Gordon-Maxwell方程解的存在性  

Existence of solutions for the Klein-Gordon-Maxwell equation under a radial symmetry potential

作　　者：郇飞 赵雷嘎 HUAN Fei;ZHAO LeiGa(Faculty of Science,Beijing University of Chemical Technology,Beijing 100029,China)

机构地区：[1]北京化工大学理学院,北京100029

出　　处：《北京化工大学学报（自然科学版）》2019年第2期123-127,共5页Journal of Beijing University of Chemical Technology(Natural Science Edition)

基　　金：国家自然科学基金(11671026)

摘　　要：研究了非线性Klein-Gordon-Maxwell方程问题■,其中参数ω>0,λ>0。当V(x)为径向对称位势并且方程的非线性项f(u)只在零点附近有定义时,可以通过变分法证明该方程解的存在性,并得到方程的解关于参数λ的依赖性。We have studied the nonlinear Klein-Gordon-Maxwell equation {-Δu+[V(x)-(ω+φ)^2]u=λf(u),x∈R^3-Δφ+u^2φ=-ωu^2,x∈R^3,where the parameter ω>0,λ>0.When V(x) is a radial symmetric potential and the nonlinear term of the equation f(u) is defined only near the zero point,the existence of solution to the equation can be proved by the calculus of variation,and the dependence on the parameter λ of the solution to the equation can be obtained.

关 键 词：Klein-Gordon-Maxwell方程 位势函数 变分方法 P-S条件 L^∞估计 

分 类 号：O176[理学—数学]