Opial’s inequality and oscillation of 2nd order equations
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- by R. C. Brown and D. B. Hinton PDF
- Proc. Amer. Math. Soc. 125 (1997), 1123-1129 Request permission
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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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
- 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