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

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Authors

HASIL Petr POSPÍŠIL Michal ŠIŠOLÁKOVÁ Jiřina VESELÝ Michal

Year of publication 2022
Type Article in Periodical
Magazine / Source Acta Mathematica Hungarica
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007/s10474-022-01218-1
Doi http://dx.doi.org/10.1007/s10474-022-01218-1
Keywords half-linear equation; linear equation; difference equation; oscillation theory; non-oscillation; Euler type; Riccati technique; Riccati equation
Description 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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