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Non-oscillation criterion for Euler type half-linear difference equations with consequences in linear case

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Abstract

We study the oscillation of Euler type half-linear difference equations with asymptotically periodic and bounded coefficients. Applying the adapted Riccati technique, we prove a non-oscillation criterion for the treated equations. Since the obtained criterion is new in several cases, we formulate many consequences explicitly. In particular, the criterion is new for intensively studied linear equations (e.g., with periodic coefficients).

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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

    P. Hasil, J. Šišoláková & M. Veselý

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina F1, 842 48, Bratislava, Slovakia

    M. Pospíšil

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    M. Pospíšil

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  1. P. Hasil
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Correspondence to M. Veselý.

Additional information

Petr Hasil and Michal Veselý are supported by Grant GA20-11846S of the Czech Science Foundation.

Michal Pospíšil is supported by the Grants VEGA-SAV 2/0127/20, VEGA 1/0358/20 and by the Slovak Research and Development Agency under the contract No. APVV-18-0308.

Jiřina Šišoláková is supported from Operational Programme Research, Development and Education, “Project Internal Grant Agency of Masaryk University”, No. CZ.02.2.69/0.0/0.0/19 073/0016943.

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Hasil, P., Pospíšil, M., Šišoláková, J. et al. Non-oscillation criterion for Euler type half-linear difference equations with consequences in linear case. Acta Math. Hungar. 166, 624–649 (2022). https://doi.org/10.1007/s10474-022-01218-1

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  • DOI: https://doi.org/10.1007/s10474-022-01218-1

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