R^N中分数阶Choquard方程的约束极小元  

Normalized Minimizers for Fractional Choquard Equations in R^N

作　　者：高彩霞 王淑丽 郭祖记 GAO Cai-xia;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,山西太原030024

出　　处：《数学的实践与认识》2020年第18期217-222,共6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中一类非线性分数阶Choquard方程在指定L^2范数下解的存在性.首先,证明了当p∈((N+α)/N,(N+α)/(N-2s))时,具有最佳常数的内插不等式;其次,对于p=(N+α+2s)/N,讨论了限制在L^2范数下方程的极小化问题,得到了能量泛函的限制极小值点的存在性.In this paper,we study the existence of solutions with a prescribed L^2-norm for a class of nonlinear fractional Choquard equations in R^N.Firstly,we prove the interpolation inequality with the best constant for p∈((N+α)/N,(N+α)/(N-2s)).Secondly,we discuss the minimization problem of the equation which is restricted in the L^2-norm and obtain the existence of minimizers of the energy functional for p=(N+α+2s)/N.

关 键 词：分数阶Choquard方程 约束解 限制极小化 

分 类 号：O175[理学—数学]