New conditionally oscillatory class of equations with coefficients containing slowly varying and periodic functions
| Autoři | |
|---|---|
| Rok publikování | 2021 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Journal of Mathematical Analysis and Applications |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://doi.org/10.1016/j.jmaa.2020.124585 |
| Doi | http://dx.doi.org/10.1016/j.jmaa.2020.124585 |
| Klíčová slova | Linear differential equations; Oscillation theory; Non-oscillation; Oscillation tests; Slowly varying functions; Periodic coefficients |
| Popis | The main result of this paper is a straightforward oscillation test for linear differential equations whose coefficients consist of products of periodic and slowly varying continuous functions. The attention is paid to the case when the slowly varying parts of the coefficients are unbounded. In particular, using the presented oscillation test, we identify a very general type of conditionally oscillatory equations together with the threshold value of the coefficients (the critical setting on the border of oscillation and non-oscillation). Hence, our results supply a class of linear equations with solved oscillation behaviour which can be used as testing equations and as a starting point to the oscillation theory of the corresponding half-linear and more general non-linear and partial differential equations with unbounded coefficients. |
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