Publication details

Non-oscillation of half-linear difference equations with asymptotically periodic coefficients

Authors

HASIL Petr JURÁNEK Jakub VESELÝ Michal

Year of publication 2019
Type Article in Periodical
Magazine / Source Acta Mathematica Hungarica
MU Faculty or unit

Faculty of Science

Citation
Web Full Text
Doi http://dx.doi.org/10.1007/s10474-019-00940-7
Keywords Riccati technique; p-Laplacian; half-linear equation; non-oscillation criterion; Riccati equation; oscillation theory; linear differential equation
Description We study oscillatory properties of half-linear difference equations with asymptotically periodic coefficients, i.e., coefficients which can be expressed as the sums of periodic sequences and sequences vanishing at infinity. Using a special variation of the discrete Riccati technique, we prove that the non-oscillation of the studied equations can be determined directly from their coefficients. Thus, the studied equations can be widely used as testing equations. Our main result is new even for linear equations with periodic coefficients. This fact is illustrated by simple corollaries and examples at the end of this paper.
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