Oscillation criterion for Euler type half-linear difference equations

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Authors

HASIL Petr VESELÝ Michal

Year of publication 2024
Type Article in Periodical
Magazine / Source Mathematical Methods in the Applied Sciences
MU Faculty or unit

Faculty of Science

Citation
Web https://onlinelibrary.wiley.com/doi/10.1002/mma.9814
Doi http://dx.doi.org/10.1002/mma.9814
Keywords difference equations; Euler type; half-linear equations; linear equations; oscillation; Riccati technique
Description We consider general classes of Euler type linear and half-linear difference equations, which are conditionally oscillatory. Applying the adapted Riccati technique, we improve known oscillation criteria for these equations. More precisely, our presented main criterion is the full oscillatory counterpart of a non-oscillation criterion. Thus, in this paper, we enlarge the set of conditionally oscillatory Euler type difference equations. We highlight that our results are new even for linear equations with periodic coefficients. This fact is documented by simple examples of such equations at the end of this paper.
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