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.

 

A comparison theorem
HTML articles powered by AMS MathViewer

by Walter Leighton and William Oo Kian Ke PDF
Proc. Amer. Math. Soc. 28 (1971), 185-188 Request permission

Abstract:

In this paper the authors consider a pair of differential equations ${y''_1} + {p_1}(x){y_1} = 0,{y''_2} + {p_2}(x){y_2} = 0$, where ${p_i}(x)$ are positive and continuous, and where solutions ${y_1}(x)$ and ${y_2}(x)$ have common consecutive zeros at $x = a$ and $x = b$. They show that if the curves $y = {p_1}(x)$ and $y = {p_2}(x)$ have a single intersection (possibly a closed subinterval) and if ${p_1}(a) > {p_2}(a),{p_2}(b) > {p_1}(b)$, the first conjugate point of $a + {\varepsilon }$ (${\varepsilon } > 0$ and small) for the second equation precedes that of the first.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34.42
  • Retrieve articles in all journals with MSC: 34.42
Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 185-188
  • MSC: Primary 34.42
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0273121-6
  • MathSciNet review: 0273121