Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Oscillation Results for Second Order Nonlinear Differential Equation with Delay and Advanced Arguments

  • Received : 2014.04.11
  • Accepted : 2015.11.03
  • Published : 2016.03.23
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Abstract

In this paper we study the oscillation criteria for the second order nonlinear differential equation with delay and advanced arguments of the form $$([x(t)+a(t)x(t-{\sigma}_1)+b(t)x(t+{\sigma}_2)]^{\alpha})^{{\prime}{\prime}}+q(t)x^{\beta}(t-{\tau}_1)+q(t)x^{\gamma}(t+{\tau}_2)=0,\;t{\geq}t_0$$ where ${\sigma}_1$, ${\sigma}_2$, ${\tau}_1$ and ${\tau}_2$ are nonnegative constants and ${\alpha}$, ${\beta}$ and ${\gamma}$ are the ratios of odd positive integers. Examples are provided to illustrate the main results.

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References

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