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Oscillation of second-order neutral delay and mixed-type dynamic equations on time scales

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Abstract

We consider the equation (r(t)(yΔ(t))γ)Δ + f(t, x(δ(t))) = 0, , where y(t) = x(t) + p(t)x(τ(t)) and γ is a quotient of positive odd integers. We present some sufficient conditions for neutral delay and mixed-type dynamic equations to be oscillatory, depending on deviating arguments τ(t) and δ(t), .

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Correspondence to Y Şahİner.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation