Oscillation results for second order half-linear neutral delay differential equations with "maxima"

Selvarangam Srinivasan, Rani Bose, Ethiraju Thandapani

Abstract


In this paper, we present some oscillation criteria for the second order half-linear neutral delay differential equation with ``maxima" of the from
\begin{equation*}
\left(r(t)((x(t)+p(t)x(\tau(t)))')^{\alpha}\right)'+q(t) \max_{[\sigma(t),\;t]}x^{\alpha}(s)=0
\end{equation*}
under the condition $\int_{t_0}^{\infty}\frac{1}{r^{1/ \alpha}(t)}dt<\infty.$ The results obtained here extend and complement to some known results in the literature. Examples are provided in support of our results.


Keywords


Oscillation, neutral delay differential equation with maxima, second order

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References


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DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.2233

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