Classification of nonoscillatory solutions of higher order neutral type difference equations

Thandapani, Ethiraju, et al. "Classification of nonoscillatory solutions of higher order neutral type difference equations." Archivum Mathematicum 031.4 (1995): 263-277. <http://eudml.org/doc/247694>.

@article{Thandapani1995,
abstract = {The authors consider the difference equation \[ \Delta ^\{m\} [y\_\{n\} - p\_\{n\} y\_\{n - k\}] + \delta q\_\{n\} y\_\{\sigma (n + m - 1)\} = 0 \qquad \mathrm \{(\ast )\}\] where $m \ge 2$, $\delta = \pm 1$, $k \in N_0 = \lbrace 0,1, 2, \dots \rbrace $, $\Delta y_\{n\} = y_\{n + 1\} - y_\{n\}$, $q_\{n\} > 0$, and $\lbrace \sigma (n)\rbrace $ is a sequence of integers with $\sigma (n) \le n$ and $\lim _\{n \rightarrow \infty \} \sigma (n) = \infty $. They obtain results on the classification of the set of nonoscillatory solutions of ($\ast $) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included.},
author = {Thandapani, Ethiraju, Sundaram, P., Graef, John R., Miciano, A., Spikes, Paul W.},
journal = {Archivum Mathematicum},
keywords = {difference equations; nonlinear; asymptotic behavior; nonoscillatory solutions; nonoscillatory solutions; higher order neutral type difference equations; asymptotics},
language = {eng},
number = {4},
pages = {263-277},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Classification of nonoscillatory solutions of higher order neutral type difference equations},
url = {http://eudml.org/doc/247694},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Thandapani, Ethiraju
AU - Sundaram, P.
AU - Graef, John R.
AU - Miciano, A.
AU - Spikes, Paul W.
TI - Classification of nonoscillatory solutions of higher order neutral type difference equations
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 4
SP - 263
EP - 277
AB - The authors consider the difference equation \[ \Delta ^{m} [y_{n} - p_{n} y_{n - k}] + \delta q_{n} y_{\sigma (n + m - 1)} = 0 \qquad \mathrm {(\ast )}\] where $m \ge 2$, $\delta = \pm 1$, $k \in N_0 = \lbrace 0,1, 2, \dots \rbrace $, $\Delta y_{n} = y_{n + 1} - y_{n}$, $q_{n} > 0$, and $\lbrace \sigma (n)\rbrace $ is a sequence of integers with $\sigma (n) \le n$ and $\lim _{n \rightarrow \infty } \sigma (n) = \infty $. They obtain results on the classification of the set of nonoscillatory solutions of ($\ast $) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included.
LA - eng
KW - difference equations; nonlinear; asymptotic behavior; nonoscillatory solutions; nonoscillatory solutions; higher order neutral type difference equations; asymptotics
UR - http://eudml.org/doc/247694
ER -