Oscillatory and non-oscillatory solutions of dynamic equations with bounded coefficients
Date
2018-01-17
Authors
Hasil, Petr
Vesely, Michal
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We analyze second-order half-linear dynamic equations on time scales. We prove oscillation and non-oscillation criteria which are sharp in the sense that the considered equations remain uncovered only for one setting of their coefficients. We continue in the research of the so-called conditional oscillation. The previously known conditionally oscillatory dynamic equations were allowed to contain only periodic coefficients. In the presented results, we deal with bounded coefficients (among others, our results cover coefficients which are periodic, almost periodic, having mean values, etc.). We point out that the results are new even for linear dynamic equations. We also provide corollaries to illustrate the novelty of our results.
Description
Keywords
Time scale, Dynamic equation, Oscillation criteria, Conditional oscillation, Riccati technique, Half-linear equation, Linear equation
Citation
Hasil, P., & Vesely, M. (2018). Oscillatory and non-oscillatory solutions of dynamic equations with bounded coefficients. <i>Electronic Journal of Differential Equations, 2018</i>(24), pp. 1-22.
Rights
Attribution 4.0 International