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In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation $${\left( {r\left( t \right)g\left( {{x^\Delta }\left( t \right)} \right)} \right)^\Delta } + p\left( t \right)f\left( {x\left( {\tau \left( t \right)} \right)} \right) = 0,$$ ( r ( t ) g ( x Δ ( t ) ) ) Δ + p ( t ) f ( x ( τ ( t ) ) ) = 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 ℕ for q > 1 and also improve most previous results. Finally, we give some examples to illustrate our main results.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Mar 15, 2017
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