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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Opial's inequality and oscillation
of 2nd order equations


Authors: R. C. Brown and D. B. Hinton
Journal: Proc. Amer. Math. Soc. 125 (1997), 1123-1129
MSC (1991): Primary 34C10; Secondary 34L05, 34L15
MathSciNet review: 1401728
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03907-5
PII: S 0002-9939(97)03907-5
Received by editor(s): October 11, 1995
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society