Oscillation and non-oscillation criteria for linear and half-linear difference equations
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Analysis and Applications |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.jmaa.2017.03.012 |
| Field | General mathematics |
| Keywords | half-linear difference equations; oscillation theory; conditional oscillation; oscillation constant; Riccati technique; adapted Riccati equation |
| Description | We find very general classes of linear and half-linear difference equations which are conditionally oscillatory. We identify the critical oscillation constant whose value implies the oscillation or non-oscillation of studied equations. Our results are divided into oscillatory and non-oscillatory theorems which determine the critical oscillation constant for coefficients given by sequences having mean values. In addition, our approach enables to analyse also the oscillatory properties of equations whose coefficients are not given by sequences with mean values. We point out that the obtained results are new even for linear equations with periodic coefficients. Such consequences are formulated at the end of this paper. |
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