RICCATI TRANSFORMATION AND NONOSCILLATION CRITERION FOR LINEAR DIFFERENCE EQUATIONS

We consider a general class of linear difference equations. Using a variation of the discrete Riccati method, we obtain a straightforward nonosciliation 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.