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Oscillation criteria for higher order nonlinear dynamic equations
Authors:Said R Grace  Taher S Hassan
Affiliation:1. +20?235876998+20?23573486;2. Department of Engineering Mathematics, Faculty of Engineering, Cairo University, , Orman, Giza, 12221 Egypt;3. Department of Mathematics, Faculty of Science, Mansoura University, , Mansoura, 35516 Egypt;4. Department of Mathematics, Faculty of Science, Hail University, , Hail, 2440 KSA
Abstract:In this paper, we will consider the higher‐order functional dynamic equations of the form urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0001 on an above‐unbounded time scale urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0002, where urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0003 and urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0004, urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0005. The function urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0006 is a rd‐continuous function such that urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0007. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.
Keywords:Asymptotic behavior  oscillation criteria  higher order  dynamic equations  time scales  34K11  39A10  39A99
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