• Title/Summary/Keyword: neutral dynamic equations of mixed type

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OSCILLATION THEOREMS FOR SECOND-ORDER MIXED-TYPE NEUTRAL DYNAMIC EQUATIONS ON SOME TIME SCALES

  • Sun, Jing
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.15-26
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    • 2012
  • Some oscillation results are presented for the second-order neutral dynamic equation of mixed type on a time scale unbounded above $$\(r(t)[x(t)+p_1(t)x(t-{\tau}_1)+p_2(t)x(t+{\tau}_2)]^{\Delta}\)^{\Delta}+q_1(t)x(t-{\tau}_3)+q_2(t)x(t+{\tau}_4)=0.$$ These criteria can be applied when $\mathbb{T}=\mathbb{R}$, $\mathbb{T}=h{\mathbb{Z}}$ and $\mathbb{T}=\mathbb{P}_{a,b}$. Two examples are also provided to illustrate the main results.