Petr Hasil, Michal Vesely
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.q
Submitted November 11, 2017. Published January 17, 2018.
Math Subject Classifications: 34N05, 26E70, 34C10, 34A30, 39A21.
Key Words: Time scale; dynamic equation; oscillation criteria;
conditional oscillation; Riccati technique;
half-linear equation; linear equation.
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Petr Hasil Department of Mathematics and Statistics Faculty of Science, Masaryk University Kotlarska 2, 611~37 Brno, Czech Republic email: hasil@mail.muni.cz |
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Michal Vesely Department of Mathematics and Statistics Faculty of Science, Masaryk University Kotlarska 2, 611~37 Brno, Czech Republic email: michal.vesely@mail.muni.cz |
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