Abstract
Using a modification of the adapted Riccati transformation, we prove an oscillation criterion for generalizations of linear and half-linear Euler difference equations. Our main result complements a large number of previously known oscillation criteria about several similar generalizations of Euler difference equations. The major part of this paper is formed by the proof of the main theorem. To illustrate the fact that the presented criterion is new even for linear equations with periodic coefficients, we finish this paper with the corresponding corollary together with concrete examples of simple equations whose oscillatory properties do not follow from previously known criteria.
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Acknowledgements
The authors gratefully acknowledge the support of this study provided by the following NIH/NIBIB Grant Numbers: R01 EB005807, R01 EB033674, R01 EB032820.
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Ludmila Linhartová is supported by Grant GA23-05242S of Czech Science Foundation and by Masaryk University under Grant MUNI/A/1457/2023.
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Hasil, P., Linhartová, L. & Veselý, M. Oscillation criterion for generalized Euler difference equations. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01460-9
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DOI: https://doi.org/10.1007/s10474-024-01460-9