Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Oscillatory Behavior of Linear Neutral Delay Dynamic Equations on Time Scales

  • Saker, Samir H. (Department of Mathematics, Faculty of Science, Mansoura University)
  • Received : 2005.07.11
  • Published : 2007.06.23
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Abstract

By employing the Riccati transformation technique some new oscillation criteria for the second-order neutral delay dynamic equation $$(y(t)+r(t)y({\tau}(t)))^{{\Delta}{\Delta}}+p(t)y(\delta(t))=0$$, on a time scale $\mathbb{T}$ are established. Our results as a special case when $\mathbb{T}=\mathbb{R}$ and $\mathbb{T}=\mathbb{N}$ improve some well known oscillation criteria for second order neutral delay differential and difference equations, and when $\mathbb{T}=q^{\mathbb{N}}$, i.e., for second-order $q$-neutral difference equations our results are essentially new and can be applied on different types of time scales. Some examples are considered to illustrate the main results.

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References

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