Comparison theorems and strong oscillation in the half-linear discrete oscillation theory

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Authors

ŘEHÁK Pavel

Year of publication 2003
Type Article in Periodical
Magazine / Source Rocky Mountain Journal of Mathematics
MU Faculty or unit

Faculty of Education

Citation
Doi http://dx.doi.org/10.1216/rmjm/1181069996
Field General mathematics
Keywords Half-linear difference equation; generalized discrete Riccati and Euler equation; comparison theorems
Description Consider the second order half--linear difference equation $$ \Delta(r_k|\Delta y_k|^{\alpha-1}\sgn\Delta y_k)+p_k|y_{k+1}|^{\alpha-1}\sgn y_{k+1}=0, \quad \alpha>1. $$ We give several various types of comparison theorems for this equation (included the so--called telescoping principle) and also for an associated generalized Riccati difference equation. In the second part we present strongly (non)oscillation criteria and related results. The paper is finished by an example, where oscillatory properties of a generalized discrete Euler equation are investigated.
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