Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the distance between zeroes
HTML articles powered by AMS MathViewer

by William T. Patula PDF
Proc. Amer. Math. Soc. 52 (1975), 247-251 Request permission

Abstract:

For the equation $x'' + q(t)x = 0$, let $x(t)$ be a solution with consecutive zeroes at $t = a$ and $t = b$. A simple inequality is proven that relates not only $a$ and $b$ to the integral of ${q^ + }(t)$ but also any point $c\epsilon (a,b)$ where $|x(t)|$ is maximized. As a corollary, it is shown that if the above equation is oscillatory and if ${q^ + }(t)\epsilon {L^p}[0,\infty ),1 \leqslant p < \infty$, then the distance between consecutive zeroes must become unbounded.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10
  • Retrieve articles in all journals with MSC: 34C10
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 247-251
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0379986-5
  • MathSciNet review: 0379986