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@article{1375985,
author = {Hasil, Petr and Veselý, Michal},
article_location = {SAN DIEGO},
article_number = {1},
doi = {http://dx.doi.org/10.1016/j.jmaa.2017.03.012},
keywords = {half-linear difference equations; oscillation theory; conditional oscillation; oscillation constant; Riccati technique; adapted Riccati equation},
language = {eng},
issn = {0022-247X},
journal = {Journal of Mathematical Analysis and Applications},
title = {Oscillation and non-oscillation criteria for linear and half-linear difference equations},
volume = {452},
year = {2017}
}
TY - JOUR
ID - 1375985
AU - Hasil, Petr - Veselý, Michal
PY - 2017
TI - Oscillation and non-oscillation criteria for linear and half-linear difference equations
JF - Journal of Mathematical Analysis and Applications
VL - 452
IS - 1
SP - 401-428
EP - 401-428
PB - ACADEMIC PRESS INC ELSEVIER SCIENCE
SN - 0022247X
KW - half-linear difference equations
KW - oscillation theory
KW - conditional oscillation
KW - oscillation constant
KW - Riccati technique
KW - adapted Riccati equation
N2 - We find very general classes of linear and half-linear difference equations which are conditionally oscillatory. We identify the critical oscillation constant whose value implies the oscillation or non-oscillation of studied equations. Our results are divided into oscillatory and non-oscillatory theorems which determine the critical oscillation constant for coefficients given by sequences having mean values. In addition, our approach enables to analyse also the oscillatory properties of equations whose coefficients are not given by sequences with mean values. We point out that the obtained results are new even for linear equations with periodic coefficients. Such consequences are formulated at the end of this paper.
ER -
HASIL, Petr and Michal VESELÝ. Oscillation and non-oscillation criteria for linear and half-linear difference equations. \textit{Journal of Mathematical Analysis and Applications}. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, vol.~452, No~1, p.~401-428. ISSN~0022-247X. doi:10.1016/j.jmaa.2017.03.012. 2017.
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