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Asymptotic and Oscillatory Behaviour of Third Order Non-linear Differential Equations with Canonical Operator and Mixed Neutral Terms

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Abstract

This paper deals with the asymptotic and oscillatory behaviour of third-order non-linear differential equations with mixed non-linear neutral terms and a canonical operator. The results are obtained via utilising integral conditions as well as comparison theorems with the oscillatory properties of first-order advanced and/or delay differential equations. The proposed theorems improve, extend, and simplify existing ones in the literature. The results are illustrated by two numerical examples.

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Acknowledgements

The authors would like to thank the editor and the five anonymous reviewers for their constructive comments and suggestions, which helped us to improve the manuscript considerably. J. Alzabut is thankful to Prince Sultan University and OSTİM Technical University for their endless support.

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Authors and Affiliations

  1. Department of Mathematics and Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia

    J. Alzabut

  2. Department of Industrial Engineering, OSTİM Technical University, 06374, Ankara, Turkey

    J. Alzabut

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

    S. R. Grace

  4. Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal, 741235, India

    S. S. Santra

  5. Department of Mathematics, Applied Science Cluster, University of Petroleum and Energy Studies (UPES), Dehradun, Uttarakhand, 248007, India

    S. S. Santra

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

    G. N. Chhatria

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  1. J. Alzabut
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Correspondence to S. S. Santra.

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Alzabut, J., Grace, S.R., Santra, S.S. et al. Asymptotic and Oscillatory Behaviour of Third Order Non-linear Differential Equations with Canonical Operator and Mixed Neutral Terms. Qual. Theory Dyn. Syst. 22, 15 (2023). https://doi.org/10.1007/s12346-022-00715-6

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