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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