一类p-Ginzburg-Landau型泛函径向极小元的零点分布问题  

Zero distribution problems of p-Ginzburg-Landau type functional radial minima

作　　者：聂东明[1] 马艳丽[1] 于萍[1] NIE Dongming;MA Yanli;YU Ping(Department of General Education, Xinhua University of Anhui, Hefei 230088, China)

机构地区：[1]安徽新华学院通识教育部,安徽合肥230088

出　　处：《南阳师范学院学报》2020年第6期20-23,共4页Journal of Nanyang Normal University

基　　金：安徽省教育厅自然科学研究项目(KJ2019A0875);安徽新华学院科研项目(2019zr005,2019zr018);安徽新华学院教研项目(2019jy013)。

摘　　要：p-Ginzburg-Landau泛函极小元的零点分布是经常研究的问题之一,但是关于零点个数与拓扑度的关系并没有确定的结论.本文研究了径向极小元的零点个数.利用罗尔定理、Hölder不等式及Pohozaev恒等式的思想推导出极小元在零点附近模的大小及单调性的结果,然后根据这一结果,把泛函极小元的零点分布在原点附近的结论推广到仅在原点位置;同时,用了一种新的比较方法得到了泛函的上界估计.The distribution of zeros of p-Ginzburg-Landau functional minima is one of the frequently studied problems,but there is no definite conclusion about the relationship between the number of zeros and the topological degree.In this paper,the number of zeros of radial minima is studied.By using Rolle’s theorem,Hölder’s inequality and Pohozaev’s identity,the results of the size and monotonicity of the modulus of the minima near the zero point are derived.Then,according to this result,the conclusion that the zero points of the functional minima are distributed near the origin is extended to only at the origin.At the same time,a new comparison method is used to obtain the upper bound estimation of the functional.

关 键 词：p-Ginzburg-Landau泛函 径向极小元 零点分布 

分 类 号：O175.2[理学—数学]