Oscillation of forced nonlinear neutral delay difference equations of first order

N. Parhi; Arun Kumar Tripathy

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 1, page 83-101
  • ISSN: 0011-4642

Abstract

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Necessary and sufficient conditions are obtained for every solution of Δ ( y n + p n y n - m ) ± q n G ( y n - k ) = f n to oscillate or tend to zero as n , where p n , q n and f n are sequences of real numbers such that q n 0 . Different ranges for p n are considered.

How to cite

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Parhi, N., and Tripathy, Arun Kumar. "Oscillation of forced nonlinear neutral delay difference equations of first order." Czechoslovak Mathematical Journal 53.1 (2003): 83-101. <http://eudml.org/doc/30761>.

@article{Parhi2003,
abstract = {Necessary and sufficient conditions are obtained for every solution of \[ \Delta (y\_\{n\}+p\_\{n\}y\_\{n-m\})\pm q\_\{n\}G(y\_\{n-k\})=f\_\{n\} \] to oscillate or tend to zero as $n\rightarrow \infty $, where $p_\{n\}$, $q_\{n\}$ and $f_\{n\}$ are sequences of real numbers such that $q_\{n\}\ge 0$. Different ranges for $p_\{n\}$ are considered.},
author = {Parhi, N., Tripathy, Arun Kumar},
journal = {Czechoslovak Mathematical Journal},
keywords = {neutral difference equations; oscillation; nonoscillation; asymptotic behaviour; oscillation; nonoscillation; asymptotic behaviour},
language = {eng},
number = {1},
pages = {83-101},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of forced nonlinear neutral delay difference equations of first order},
url = {http://eudml.org/doc/30761},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Parhi, N.
AU - Tripathy, Arun Kumar
TI - Oscillation of forced nonlinear neutral delay difference equations of first order
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 83
EP - 101
AB - Necessary and sufficient conditions are obtained for every solution of \[ \Delta (y_{n}+p_{n}y_{n-m})\pm q_{n}G(y_{n-k})=f_{n} \] to oscillate or tend to zero as $n\rightarrow \infty $, where $p_{n}$, $q_{n}$ and $f_{n}$ are sequences of real numbers such that $q_{n}\ge 0$. Different ranges for $p_{n}$ are considered.
LA - eng
KW - neutral difference equations; oscillation; nonoscillation; asymptotic behaviour; oscillation; nonoscillation; asymptotic behaviour
UR - http://eudml.org/doc/30761
ER -

References

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  1. 10.1006/jmaa.1997.5341, J. Math. Anal. Appl. 221 (1998), 73–91. (1998) MR1619135DOI10.1006/jmaa.1997.5341
  2. 10.1080/00036818908839876, Appl. Anal. 33 (1989), 243–251. (1989) MR1030111DOI10.1080/00036818908839876
  3. Oscillation of neutral difference equations with variable coefficient, In: Differencial Equations: Stability and Control, Marcel Dekker, 1990, pp. 165–178. (1990) MR1096752
  4. Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991. (1991) MR1168471
  5. 10.1016/0022-247X(91)90278-8, J.  Math. Anal. Appl. 158 (1991), 213–233. (1991) MR1113411DOI10.1016/0022-247X(91)90278-8
  6. 10.1016/0022-247X(92)90342-B, J.  Math. Anal. Appl. 166 (1992), 272–287. (1992) MR1159653DOI10.1016/0022-247X(92)90342-B
  7. Oscillation criteria for forced non-linear neutral delay difference equations of first order, Differential Equations Dynam. Systems 8 (2000), 81–97. (2000) MR1858770
  8. 10.1006/jmaa.2000.7315, J.  Math. Anal. Appl. 256 (2001), 525–541. (2001) MR1821755DOI10.1006/jmaa.2000.7315
  9. Asymptotic behaviour and oscillation of solutions of neutral delay-difference equations of arbitary order, Math. Slovaca 47 (1997), 539–551. (1997) MR1635228
  10. Oscillation criteria and comparision theorems for delay-difference equations, Fasc. Math. 25 (1995), 13–32. (1995) MR1339622

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