带有临界项的薛定谔-泊松系统的基态解  

Ground state solution to Schrodinger-Poisson system with critical term

作　　者：董思雨 冯晓晶 DONG Siyu;FENG Xiaojing(School of Mathematical Science, Shanxi University, Taiyuan 030006, China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《纺织高校基础科学学报》2020年第1期75-80,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11671239,11801338);山西省自然科学基金(201801D211001,201801D121002,201801D2210)。

摘　　要：研究带有双临界项的薛定谔-泊松系统基态解的存在性,其中位势函数和非线性项是渐近周期函数。根据介值定理获得了Nehari流形的一些性质,并利用分析技巧估计了Nehari流形上的极小值。运用球面映射得到了极小化序列为相应泛函的(PS)序列。同时结合逼近和集中紧性原理证明系统基态解的存在性。The existence of ground state solution for the Poisson system with double critical terms is studied,when the potential function and the nonlinear term are asymptotically periodic.Some properties of Nehari manifold are obtained by intermediate value theorem,and minimum value of Nehari manifold is estimated by using analysis techniques.The minimization sequence is obtained as corresponding functional(PS)sequence by using spherical mapping.Meanwhile,combining with approximation and the concentration-compactness principle,the system has a ground state solution.

关 键 词：薛定谔-泊松系统 NEHARI流形 基态解 集中紧性原理 

分 类 号：O177.91[理学—数学] O175.2[理学—基础数学]