Riccati transformation and nonoscillation criterion for linear difference equations

Fujimoto, Kōdai; Hasil, Petr; Veselý, Michal

doi:10.1090/proc/15072

Riccati transformation and nonoscillation criterion for linear difference equations
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by Kōdai Fujimoto, Petr Hasil and Michal Veselý PDF

Proc. Amer. Math. Soc. 148 (2020), 4319-4332 Request permission

Abstract:

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

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