B~N中预定边界平均曲率问题的无穷多解的存在性

发布时间：2018-05-20 03:31

本文选题：预定平均边界曲率问题 + 无穷多解　；参考：《华东师范大学》2017年硕士论文

【摘要】：预定边界平均曲率问题是共形几何中的一类重要问题。本文主要研究了BN上预定边界平均曲率问题的等价方程其中K(x)是RN-1上的有界连续函数,有一串趋向于正无穷的严格极大值点zj,并且在每个极大值点zj的小邻域内有如下形式的展开本文通过有限维约化方法,将求解能量泛函I(u)的临界点问题转化为求解定义在有限维区域上泛函的临界点问题,从而得到该方程的无穷多个正解,且这些解都有两个极大值点,这两个极大值点之间的距离很大。
[Abstract]:The mean curvature problem is an important problem in conformal geometry. In this paper, we study the equivalent equation of the mean curvature problem with predetermined boundary on BN, where Knx) is a bounded continuous function on RN-1. There is a series of strict maximum points zjj which tend to be positive infinity, and there are the following forms of expansion in the small neighborhood of every maximum point zj. In this paper, the finite dimension reduction method is used. The critical point problem for solving the energy functional is transformed into a critical point problem for solving a functional defined in a finite dimensional domain, and the infinite positive solutions of the equation are obtained, all of which have two maximum points. The distance between the two maximum points is very large.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O186.1

【参考文献】