On an inequality of Nehari

Abstract

In a private communication with one of the authors, Professor Nehari has indicated that the inequality is undecided since the argument given in [I] that Theorem II implies Theorem I is incorrect. It is the purpose of this note to show that (1) is correct for n =2. In fact, we prove a stronger result for (2) y+gy'+fy =O. THEOREM. Let a and b be successive zeros of a nontrivial solution to (2) where f and g are integrable. Then