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@article{1804592, author = {Hasil, Petr and Veselý, Michal}, article_number = {6}, doi = {http://dx.doi.org/10.1007/s00013-021-01649-2}, keywords = {Linear equation; Difference equation; Oscillation criterion; Conditional oscillation; Riccati technique; Riccati equation}, language = {eng}, issn = {0003-889X}, journal = {Archiv der Mathematik}, title = {Riccati technique and oscillation of linear second-order difference equations}, url = {https://doi.org/10.1007/s00013-021-01649-2}, volume = {117}, year = {2021} }
TY - JOUR ID - 1804592 AU - Hasil, Petr - Veselý, Michal PY - 2021 TI - Riccati technique and oscillation of linear second-order difference equations JF - Archiv der Mathematik VL - 117 IS - 6 SP - 657-669 EP - 657-669 PB - Springer Nature Switzerland AG SN - 0003889X KW - Linear equation KW - Difference equation KW - Oscillation criterion KW - Conditional oscillation KW - Riccati technique KW - Riccati equation UR - https://doi.org/10.1007/s00013-021-01649-2 N2 - 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. ER -
HASIL, Petr a Michal VESELÝ. Riccati technique and oscillation of linear second-order difference equations. \textit{Archiv der Mathematik}. Springer Nature Switzerland AG, 2021, roč.~117, č.~6, s.~657-669. ISSN~0003-889X. Dostupné z: https://dx.doi.org/10.1007/s00013-021-01649-2.
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