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Riccati technique and oscillation of linear second-order difference equations

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Abstract

In this paper, we analyse oscillatory properties of a general class of linear difference equations. Applying the modified Riccati technique, we prove an oscillation criterion for the studied equations and we formulate its consequences. In contrast to many known criteria, in the presented results, there are not considered any auxiliary sequences. The results are based directly on the coefficients of the treated equations, i.e., the obtained results are easy to use. In addition, recently, we have proved a non-oscillatory counterpart of the presented criterion. The combination implies that the studied equations are conditionally oscillatory.

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Acknowledgements

Petr Hasil and Michal Veselý are supported by Grant GA20-11846S of the Czech Science Foundation. The authors would like to thank the reviewer for valuable comments that improved the presentation of the used method.

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Authors and Affiliations

  1. Department of Mathematics and Statistics Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Petr Hasil & Michal Veselý

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  1. Petr Hasil
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  2. Michal Veselý
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Correspondence to Michal Veselý.

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Hasil, P., Veselý, M. Riccati technique and oscillation of linear second-order difference equations. Arch. Math. 117, 657–669 (2021). https://doi.org/10.1007/s00013-021-01649-2

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  • DOI: https://doi.org/10.1007/s00013-021-01649-2

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