Riccati technique and oscillation of linear second-order difference equations

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Authors	HASIL Petr VESELÝ Michal
Year of publication	2021
Type	Article in Periodical
Magazine / Source	Archiv der Mathematik
MU Faculty or unit	Faculty of Science
Citation
Web	https://doi.org/10.1007/s00013-021-01649-2
Doi	http://dx.doi.org/10.1007/s00013-021-01649-2
Keywords	Linear equation; Difference equation; Oscillation criterion; Conditional oscillation; Riccati technique; Riccati equation
Description	In this paper, we analyse oscillatory properties of a general class of linear difference equations. Applying the modified Riccati technique, we prove an oscillation criterion for the studied equations and we formulate its consequences. In contrast to many known criteria, in the presented results, there are not considered any auxiliary sequences. The results are based directly on the coefficients of the treated equations, i.e., the obtained results are easy to use. In addition, recently, we have proved a non-oscillatory counterpart of the presented criterion. The combination implies that the studied equations are conditionally oscillatory.
Related projects:	Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace