Oscillation and nonoscillation of second order neutral delay difference equations

• Volume: 53, Issue: 4, page 935-947
• ISSN: 0011-4642

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Abstract

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Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation $\Delta \left({c}_{n}\Delta \left({y}_{n}+{p}_{n}{y}_{n-k}\right)\right)+{q}_{n}{y}_{n+1-m}^{\beta }=0,\phantom{\rule{1.0em}{0ex}}n\ge {n}_{0}$ where $k$, $m$ are positive integers and $\beta$ is a ratio of odd positive integers are established, under the condition ${\sum }_{n={n}_{0}}^{\infty }\frac{1}{{c}_{n}}<\infty .$

How to cite

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Thandapani, Ethiraju, and Mahalingam, K.. "Oscillation and nonoscillation of second order neutral delay difference equations." Czechoslovak Mathematical Journal 53.4 (2003): 935-947. <http://eudml.org/doc/30826>.

@article{Thandapani2003,
abstract = {Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation $\Delta (c\_n\Delta (y\_n+p\_ny\_\{n-k\}))+q\_ny\_\{n+1-m\}^\beta =0,\quad n\ge n\_0$ where $k$, $m$ are positive integers and $\beta$ is a ratio of odd positive integers are established, under the condition $\sum _\{n=n_0\}^\{\infty \}\frac\{1\}\{c_n\}<\{\infty \}.$},
author = {Thandapani, Ethiraju, Mahalingam, K.},
journal = {Czechoslovak Mathematical Journal},
keywords = {neutral delay; difference equation; oscillation; neutral delay; difference equation; oscillation},
language = {eng},
number = {4},
pages = {935-947},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation and nonoscillation of second order neutral delay difference equations},
url = {http://eudml.org/doc/30826},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Thandapani, Ethiraju
AU - Mahalingam, K.
TI - Oscillation and nonoscillation of second order neutral delay difference equations
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 935
EP - 947
AB - Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation $\Delta (c_n\Delta (y_n+p_ny_{n-k}))+q_ny_{n+1-m}^\beta =0,\quad n\ge n_0$ where $k$, $m$ are positive integers and $\beta$ is a ratio of odd positive integers are established, under the condition $\sum _{n=n_0}^{\infty }\frac{1}{c_n}<{\infty }.$
LA - eng
KW - neutral delay; difference equation; oscillation; neutral delay; difference equation; oscillation
UR - http://eudml.org/doc/30826
ER -

References

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1. Difference Equations and Inequalities, Secon Edition, Marcel Dekker, New York, 2000. (2000) MR1740241
2. Advanced Topics in Difference Equations, Kluwer Publ., Dordrecht, 1997. (1997) MR1447437
3. Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, 1991. (1991) MR1147908
4. Classification and existence of positive solutions of second order nonlinear neutral difference equations, Funk. Ekv. 40 (1997), 371–393. (1997)
5. 10.1006/jmaa.1993.1052, J. Math. Anal. Appl. 173 (1993), 58–68. (1993) Zbl0780.39006MR1205909DOI10.1006/jmaa.1993.1052

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