Schrodinger-Possion方程的约束极小解  

The Constrained Minimizers of Schrodinger-Possion Equations

作　　者：周晓敏 王淑丽 郭祖记 ZHOU Xiao-min;WANG Shu-li;GUO Zu-ji(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院

出　　处：《数学的实践与认识》2019年第21期243-250,共8页Mathematics in Practice and Theory

基　　金：国家自然科学青年基金(11601363);山西省自然科学基金(201601D102001)

摘　　要：研究R^N中一类Schrodinger-Possion方程约束极小解的存在性与非存在性.通过对该方程非线性项部分所含参数p的分类讨论,利用极小化序列方法,Ekeland’s变分原理,消失引理,Pohozaev’s恒等式,Gagliardo-Nirenberg不等式,Hardy-Littewood-Sobolev不等式等变分工具,最终证明了相应的结论.In this paper,we concerned with the existence and the nonexistence of constrained minimizers for a class of Schrodinger-Possion Equations.By means of the categorized discussion for parameter p in the nonlinearity of the equation,the corresponding conclusion was proved by using minimizing sequence method,Ekeland variational principle,Vanishing Lemma,the Gagliardo-Nirenberg identity,the Haxdy-Littewood-Sobolev inequality and the Pohozaev identity in the variational methods.

关 键 词：Schrodinger-Possion方程 变分法 极小化序列 约束极小元 

分 类 号：O15[理学—数学]