一类带临界指数的Schr dinger-Poisson系统的正解的存在性

Existence of Positive Solutionsfor a Class of Schr dinger-Poisson System with Critical Exponent

Schr dinger-Poisson系统是由Schr dinger方程和Poisson方程耦合在一起所得,它具有很强的物理背景,主要用来研究微观物质在电场中的运动规律。本文考虑有界区域上一类带临界指数的Schr dinger-Poisson系统,利用山路定理和Ekeland变分原理,获得了该系统至少存在2个正解。

Schr dinger-Poisson system is obtained by coupling Schr dinger equation and Poisson equation.With a strong physical background,it is mainly used to study the motion law of micro matter in electric field.In this paper,a class of Schr dinger-Poisson system with critical exponents on bounded domains is considered and two positive solutions are obtained by Mountain Pass Theorem and Ekeland variational principle.