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

Oscillation criteria of second order half linear delay dynamic equations on time scales 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-017-0639-4
Publisher site
See Article on Publisher Site

Abstract

In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation $${\left( {r\left( t \right)g\left( {{x^\Delta }\left( t \right)} \right)} \right)^\Delta } + p\left( t \right)f\left( {x\left( {\tau \left( t \right)} \right)} \right) = 0,$$ ( 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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 15, 2017

References