1. On a Conjecture of Bahri—Xu
- Author
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Zhi Qin Lu, Jian Quan Ge, Hong Chen, and Kai Jia
- Subjects
Discrete mathematics ,Conjecture ,Applied Mathematics ,General Mathematics ,Order (group theory) ,Mathematics - Abstract
In order to study the Yamabe changing-sign problem, Bahri and Xu proposed a conjecture which is a universal inequality for p points in ℝm. 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.
- Published
- 2021