Conditional oscillation of half-linear Euler-type dynamic equations on time scales

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článek v časopise ve Web of Science, Jimp
Popis

We investigate second-order half-linear Euler-type dynamic equations on time scales with positive periodic coefficients. We show that these equations are conditionally oscillatory, i.e., there exists a sharp borderline (a constant given by the coefficients of the given equation) between oscillation and non-oscillation of these equations. In addition, we explicitly find this so-called critical constant. In the cases that the time scale is reals or integers, our result corresponds to the classical results as well as in the case that the coefficients are replaced by constants and we take into account the linear equations. An example and corollaries are provided as well.

Klíčová slova
time scale
dynamic equation
oscillation theory
conditional oscillation
oscillation constant
Euler equation
Riccati technique
half-linear equation