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Oscillation criteria for solution of hyperbolic delay dynamic equations with time and spatial variables on arbitrary time scales

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Abstract

Oscillatory behavior of a hyperbolic delay partial dynamic equation with time and spatial variables defined on arbitrary time scales is studied in this article. The Green’s identity on an arbitrary time scale is presented. Using that identity and Riccati transformation, several oscillation criteria for the concern dynamic equation with Neumann boundary condition is established. Examples are provided to illustrate our results.

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Acknowledgements

The authors express their sincere gratitude to the editors and anonymous referee for the careful reading of the original manuscript and useful comments that helped to improve the presentation of the results. The third author was funded under FIST programme SR/FST/MS1-115/2016 by Department of Science and Technology, India.

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Authors and Affiliations

  1. Department of Mathematics, Muthayammal College of Engineering, Rasipuram, 637408, India

    R. Ramesh

  2. Department of Mathematics, Sona College of Technology, Salem, 636005, India

    S. Harikrishnan

  3. Department of Mathematics, Periyar University, Salem, 636011, India

    P. Prakash

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  1. R. Ramesh
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  2. S. Harikrishnan
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  3. P. Prakash
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Correspondence to P. Prakash.

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Ramesh, R., Harikrishnan, S. & Prakash, P. Oscillation criteria for solution of hyperbolic delay dynamic equations with time and spatial variables on arbitrary time scales. J. Appl. Math. Comput. 67, 207–219 (2021). https://doi.org/10.1007/s12190-020-01478-6

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  • DOI: https://doi.org/10.1007/s12190-020-01478-6

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