Publication details

Riccati technique and oscillation of linear second-order difference equations

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Year of publication 2021
Type Article in Periodical
Magazine / Source Archiv der Mathematik
MU Faculty or unit

Faculty of Science

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.
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