On a Conjecture of Bahri–Xu  

作　　者：Hong CHEN Jian Quan GE Kai JIA Zhi Qin LU 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China [2]School of Mathematical Sciences,Laboratory of Mathematics and Complex Systems,Beijing Normal University,Beijing 100875,P.R.China [3]Department of Mathematics,University of California,Irvine,Irvine,CA 92697,USA

出　　处：《Acta Mathematica Sinica,English Series》2021年第11期1721-1742,共22页数学学报（英文版）

基　　金：partially supported by Beijing Natural Science Foundation(Grant No.Z190003);partially supported by National Sciences Foundation of USA(Grant No.DMS-19-08513)。

摘　　要：In order to study the Yamabe changing-sign problem,Bahri and Xu proposed a conjecture which is a universal inequality for p points in R^(m).They have verified the conjecture for p≤3.In this paper,we first simplify this conjecture by giving two sufficient and necessary conditions inductively.Then we prove the conjecture for the basic case m=1 with arbitrary p.In addition,for the cases when p=4,5 and m≥2,we manage to reduce them to the basic case m=1 and thus prove them as well.

关 键 词：Yamabe PROBLEM Bahri-Xu CONJECTURE 

分 类 号：O178[理学—数学]