Oscillation criteria for third order nonlinear delay dynamic equations on time scales

Tom 99 / 2010

Zhenlai Han, Tongxing Li, Shurong Sun, Fengjuan Cao Annales Polonici Mathematici 99 (2010), 143-156 MSC: 34C10, 34K11, 34N05, 39A21. DOI: 10.4064/ap99-2-3

Streszczenie

By means of Riccati transformation technique, we establish some new oscillation criteria for third-order nonlinear delay dynamic equations $$ ((x^{\Delta\Delta}(t))^\gamma)^\Delta+p(t)x^\gamma(\tau(t))=0 $$ on a time scale $\mathbb{T};$ here $\gamma>0$ is a quotient of odd positive integers and $p$ a real-valued positive rd-continuous function defined on $\mathbb{T}.$ Our results not only extend and improve the results of T. S. Hassan [Math. Comput. Modelling 49 (2009)] but also unify the results on oscillation of third-order delay differential equations and third-order delay difference equations.

Autorzy

  • Zhenlai HanSchool of Science
    University of Jinan
    Jinan, Shandong 250022, P.R. China
    and
    School of Control Science and Engineering
    Shandong University
    Jinan, Shandong 250061, P.R. China
    e-mail
  • Tongxing LiSchool of Science
    University of Jinan
    Jinan, Shandong 250022, P.R. China
    e-mail
  • Shurong SunSchool of Science
    University of Jinan
    Jinan, Shandong 250022, P.R. China
    and
    Department of Mathematics and Statistics
    Missouri University of Science and Technology
    Rolla, MO 65409-0020, U.S.A.
    e-mail
  • Fengjuan CaoSchool of Science
    University of Jinan
    Jinan, Shandong 250022, P.R. China
    e-mail

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