Riccati Transformation and Non-Oscillation Criterion for Half-Linear Difference Equations

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Authors	FUJIMOTO Kodai HASIL Petr VESELÝ Michal
Year of publication	2024
Type	Article in Periodical
Magazine / Source	Bulletin of the Malaysian Mathematical Sciences Society
MU Faculty or unit	Faculty of Science
Citation
Web	https://link.springer.com/article/10.1007/s40840-024-01745-w
Doi	http://dx.doi.org/10.1007/s40840-024-01745-w
Keywords	Half-linear equation; Difference equation; Non-oscillation; Oscillation theory; Riccati equation
Description	In this paper, we study a general class of half-linear difference equations. Applying a version of the discrete Riccati transformation, we prove a non-oscillation criterion for the analyzed equations. In the formulation of the criterion, we do not use auxiliary sequences, but we consider directly the coefficients of the treated equations. Since the obtained criterion is new in many cases, we also formulate new simple corollaries and mention illustrative examples.
Related projects:	Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace