Oscillation constants for half-linear difference equations with coefficients having mean values

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Authors

VESELÝ Michal HASIL Petr

Year of publication 2015
Type Article in Periodical
Magazine / Source Advances in Difference Equations
MU Faculty or unit

Faculty of Science

Citation
Web http://www.advancesindifferenceequations.com/content/2015/1/210
Doi http://dx.doi.org/10.1186/s13662-015-0544-1
Field General mathematics
Keywords half-linear difference equation; oscillation theory; conditional oscillation; oscillation constant; Euler equation; Riccati technique
Description We investigate second order half-linear Euler type difference equations whose coefficients have mean values. We show that these equations are conditionally oscillatory and we explicitly identify the corresponding oscillation constants given by the coefficients. Our results generalize the known ones concerning equations with positive constant, periodic, or (asymptotically) almost periodic coefficients. We also demonstrate the obtained results on examples and we give corollaries. In particular, we get new results even for linear difference equations.
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