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New Oscillation Criteria for Second Order Quasilinear Neutral Delay Differential Equations

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Abstract

The authors present some new sufficient conditions for the oscillation of second order quasilinear neutral delay differential equation

$$\begin{aligned} (a(t)(z'(t))^{\beta })'+q(t)x^{\gamma }(\sigma (t))=0,\;t\ge t_0>0, \end{aligned}$$

where \(z(t)=x(t)+p(t)x(\tau (t))\). Our oscillation results depend on only one condition and essentially improve, complement and simplify many related ones in the literature. Examples are provided to illustrate the value of the main results.

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Acknowledgements

The authors sincerely thank the Reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original paper. This work was partially supported by FCT and CEMAT by the projects UIDB/04621/2020 and UIDP/04621/2020.

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Authors and Affiliations

  1. Department of Mathematics, SRM University, Ramapuram Campus, Chennai, 600 089, India

    N. Prabaharan & C. Dharuman

  2. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, 600 005, India

    E. Thandapani

  3. Departamento de Ciencias Exatas e Naturais, Academia Militar, 2720-113, Amadora, Portugal

    S. Pinelas

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  1. N. Prabaharan
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  2. C. Dharuman
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  4. S. Pinelas
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Correspondence to S. Pinelas.

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Prabaharan, N., Dharuman, C., Thandapani, E. et al. New Oscillation Criteria for Second Order Quasilinear Neutral Delay Differential Equations. Differ Equ Dyn Syst 31, 945–956 (2023). https://doi.org/10.1007/s12591-020-00550-8

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