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Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations

Author

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  • Zuzana Pátíková

    (Department of Mathematics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 760 05 Zlín, Czech Republic)

  • Simona Fišnarová

    (Department of Mathematics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic)

Abstract

We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is ensured by the divergence of a certain integral. The second one provides the condition of the oscillation in the case where the relevant integral converges, and it can be seen as a Hille–Nehari-type criterion. The use of the results is shown in several examples, in which the Euler-type equation and its perturbations are considered.

Suggested Citation

  • Zuzana Pátíková & Simona Fišnarová, 2021. "Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:235-:d:486733
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    References listed on IDEAS

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    1. Chatzarakis, G.E. & Džurina, J. & Jadlovská, I., 2019. "New oscillation criteria for second-order half-linear advanced differential equations," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 404-416.
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