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Oscillation criteria of second order half linear delay dynamic equations on time scales

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Abstract

In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation

$${\left( {r\left( t \right)g\left( {{x^\Delta }\left( t \right)} \right)} \right)^\Delta } + p\left( t \right)f\left( {x\left( {\tau \left( t \right)} \right)} \right) = 0,$$

on a time scale T. Oscillation behavior of this equation is not studied before. Our results not only apply on differential equations when T=ℝ, difference equations when T=ℕ but can be applied on different types of time scales such as when T=q for q > 1 and also improve most previous results. Finally, we give some examples to illustrate our main results.

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Correspondence to Heba A. Hassan.

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Agwo, H.A., Khodier, A.M.M. & Hassan, H.A. Oscillation criteria of second order half linear delay dynamic equations on time scales. Acta Math. Appl. Sin. Engl. Ser. 33, 83–92 (2017). https://doi.org/10.1007/s10255-017-0639-4

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  • DOI: https://doi.org/10.1007/s10255-017-0639-4

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