Opial's type inequalities on time scales and some applications

Volume 104 / 2012

S. H. Saker Annales Polonici Mathematici 104 (2012), 243-260 MSC: 26A15, 26D10, 26D15, 39A13, 34A40, 34K11, 34C10. DOI: 10.4064/ap104-3-3

Abstract

We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm–Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential equations, give some new results for difference equations and yield conditions for disfocality for second order dynamic equations on time scales.

Authors

  • S. H. SakerCollege of Science Research Centre
    King Saud University
    P.O. Box 2455
    Riyadh 11451, Saudi Arabia
    e-mail
    e-mail

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