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A generalization of Opial’s inequality and applications to second-order dynamic equations

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Abstract

In this paper, we extend to arbitrary time scales some results of [Proc. Amer. Math. Soc., vol. 125, no. 4, pp. 1123–1129, (1997)], where R. C. Brown and D. B. Hinton investigate oscillation of a second-order differential equation. We also provide some examples on nontrivial time scales to illustrate the applicability of the results.

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Authors and Affiliations

  1. Faculty of Science and Arts, Department of Mathematics, ANS Campus, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey

    Başak Karpuz

  2. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA

    Billûr Kaymakçalan

  3. Faculty of Science and Arts, Department of Mathematics, ANS Campus, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey

    Özkan Öcalan

Authors
  1. Başak Karpuz
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  2. Billûr Kaymakçalan
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  3. Özkan Öcalan
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Correspondence to Başak Karpuz.

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Karpuz, B., Kaymakçalan, B. & Öcalan, Ö. A generalization of Opial’s inequality and applications to second-order dynamic equations. Differ Equ Dyn Syst 18, 11–18 (2010). https://doi.org/10.1007/s12591-010-0001-2

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  • DOI: https://doi.org/10.1007/s12591-010-0001-2

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