Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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OSCILLATION OF SECOND ORDER SUBLINEAR NEUTRAL DELAY DYNAMIC EQUATIONS VIA RICCATI TRANSFORMATION

  • Received : 2017.10.07
  • Accepted : 2018.02.14
  • Published : 2018.05.30
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Abstract

In this work, we establish oscillation of the second order sublinear neutral delay dynamic equations of the form:$$(r(t)((x(t)+p(t)x({\tau}(t)))^{\Delta})^{\gamma})^{\Delta}+q(t)x^{\gamma}({\alpha}(t))+v(t)x^{\gamma}({\eta}(t))=0$$ on a time scale T by means of Riccati transformation technique, under the assumptions $${\displaystyle\smashmargin{2}{\int\nolimits^{\infty}}_{t_0}}\({\frac{1}{r(t)}}\)^{\frac{1}{\gamma}}{\Delta}t={\infty}$$, and ${\displaystyle\smashmargin{2}{\int\nolimits^{\infty}}_{t_0}}\({\frac{1}{r(t)}}\)^{\frac{1}{\gamma}}{\Delta}t$ < ${\infty}$, for various ranges of p(t), where 0 < ${\gamma}{\leq}1$ is a quotient of odd positive integers.

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Acknowledgement

Supported by : Rajiv Gandhi National Fellowship (UGC)

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