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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Opial’s inequality and oscillation of 2nd order equations
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by R. C. Brown and D. B. Hinton
Proc. Amer. Math. Soc. 125 (1997), 1123-1129
DOI: https://doi.org/10.1090/S0002-9939-97-03907-5

Abstract:

For a second-order differential equation, we obtain from Opial’s inequality lower bounds for the spacing between two zeros of a solution or between a zero of a solution and a zero of its derivative. These bounds are expressed in terms of antiderivatives of the potential, and in particular we derive some new Liapunov type inequalities from them.
References
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Bibliographic Information
  • R. C. Brown
  • Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487
  • Email: dbrown@mathdept.as.ua.edu
  • D. B. Hinton
  • Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487
  • Email: hinton@novell.math.utk.edu
  • Received by editor(s): October 11, 1995
  • Communicated by: Hal L. Smith
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1123-1129
  • MSC (1991): Primary 34C10; Secondary 34L05, 34L15
  • DOI: https://doi.org/10.1090/S0002-9939-97-03907-5
  • MathSciNet review: 1401728