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Nonlinear Second Order Delay Dynamic Equations on Time Scales: New Oscillatory Criteria

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Abstract

In the paper, we present some new oscillation results for the second order nonlinear delay dynamic equation of the form

$$\begin{aligned} \left( r(\theta )(z^{\Delta }(\theta ))^{\alpha }\right) ^{\Delta } +q(\theta )z^{\nu }(\omega (\theta ))=0\;\text {for}\;\theta \in {\mathbb {T}}_{0}=[\theta _{0},\infty )\cap {\mathbb {T}}. \end{aligned}$$

We derive new monotonic properties of the nonoscillatory solutions and utilizing them to linearize the considered equation. The presented results are verified by some illustrative examples.

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Acknowledgements

We would like to thank the three anonymous reviewers for their constructive comments and suggestions, which helped us improve the manuscript considerably. The work of G. N. Chhatria is supported by the University Grants Commission (UGC), New Delhi, India, through Letter No. F1-17.1/2017-18/RGNF-2017-18-SC-ORI-35849, dated July 11th, 2017.

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Authors and Affiliations

  1. Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza, 12221, Egypt

    Said R. Grace

  2. Department of Mathematics, Sambalpur University, Sambalpur, 768019, India

    G. N. Chhatria

  3. School of Mathematical and Statistical Sciences, Indian Institute of Technology, Mandi, Himachal Pradesh, 175005, India

    Syed Abbas

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Grace, S.R., Chhatria, G.N. & Abbas, S. Nonlinear Second Order Delay Dynamic Equations on Time Scales: New Oscillatory Criteria. Qual. Theory Dyn. Syst. 22, 102 (2023). https://doi.org/10.1007/s12346-023-00800-4

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