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Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales

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  • Shao-Yan Zhang
  • Qi-Ru Wang

Abstract

This paper is concerned with oscillation of second-order forced functional dynamic equations of the form on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.

Suggested Citation

  • Shao-Yan Zhang & Qi-Ru Wang, 2014. "Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnddns:684068
    DOI: 10.1155/2014/684068
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    Cited by:

    1. Taher S. Hassan & Clemente Cesarano & Rami Ahmad El-Nabulsi & Waranont Anukool, 2022. "Improved Hille-Type Oscillation Criteria for Second-Order Quasilinear Dynamic Equations," Mathematics, MDPI, vol. 10(19), pages 1-18, October.
    2. Ya-Ru Zhu & Zhong-Xuan Mao & Jing-Feng Tian & Ya-Gang Zhang & Xin-Ni Lin, 2022. "Oscillation and Nonoscillatory Criteria of Higher Order Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 10(5), pages 1-17, February.
    3. Karpuz, Başak, 2019. "Hille–Nehari theorems for dynamic equations with a time scale independent critical constant," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 336-351.
    4. Chandrasekaran, E. & Chatzarakis, George E. & Palani, G. & Thandapani, E., 2020. "Oscillation criteria for advanced difference equations of second order," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    5. Grace, Said R. & Negi, Shekhar Singh & Abbas, Syed, 2022. "New oscillatory results for non-linear delay dynamic equations with super-linear neutral term," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Taher S. Hassan & Qingkai Kong & Bassant M. El-Matary, 2023. "Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    7. Yong Zhou & Bashir Ahmad & Ahmed Alsaedi, 2019. "Structure of Non-Oscillatory Solutions for Second Order Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 7(8), pages 1-12, July.

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