Publication details

Oscillatory and non-oscillatory solutions of dynamic equations with bounded coefficients

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Year of publication 2018
Type Article in Periodical
Magazine / Source Electronic Journal of Differential Equations
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords time scale; dynamic equation; oscillation criteria; conditional oscillation; Riccati technique; half-linear equation; linear equation
Description We analyse 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.
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