On a Conjecture of Bahri—Xu

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.