Riccati transformation and non-oscillation criterion for linear difference equations

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Authors	FUJIMOTO Kodai HASIL Petr VESELÝ Michal
Year of publication	2020
Type	Article in Periodical
Magazine / Source	Proceedings of the American Mathematical Society
MU Faculty or unit	Faculty of Science
Citation
Web	https://doi.org/10.1090/proc/15072
Doi	http://dx.doi.org/10.1090/proc/15072
Keywords	linear equations; difference equations; Riccati method; non-oscillation; oscillation theory
Description	We consider a general class of linear difference equations. Using a variation of the discrete Riccati method, we obtain a straightforward non-oscillation criterion for the treated equations. In contrast to a number of known criteria, we do not need to consider any auxiliary sequences. We use the coefficients of the treated equations directly. To illustrate the novelty and the usage of the presented criterion, we provide corollaries and examples.
Related projects:	Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace