Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation

Ethiraju Thandapani; L. Ramuppillai

Kybernetika (1999)

  • Volume: 35, Issue: 4, page [499]-506
  • ISSN: 0023-5954

Abstract

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In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form Δ 2 y n - 1 + q n y σ ( n ) γ = g n , where γ is a quotient of odd positive integers, in the superlinear case ( γ > 1 ) and in the sublinear case ( γ < 1 ) .

How to cite

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Thandapani, Ethiraju, and Ramuppillai, L.. "Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation." Kybernetika 35.4 (1999): [499]-506. <http://eudml.org/doc/33443>.

@article{Thandapani1999,
abstract = {In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form $\Delta ^2y_\{n-1\}+q_ny_\{\sigma (n)\}^\gamma =g_n$, where $\gamma $ is a quotient of odd positive integers, in the superlinear case $(\gamma >1)$ and in the sublinear case $(\gamma <1)$.},
author = {Thandapani, Ethiraju, Ramuppillai, L.},
journal = {Kybernetika},
keywords = {oscillation; nonlinear delay difference equation; Emden-Fowler type; oscillation; nonlinear delay difference equation; Emden-Fowler type},
language = {eng},
number = {4},
pages = {[499]-506},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation},
url = {http://eudml.org/doc/33443},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Thandapani, Ethiraju
AU - Ramuppillai, L.
TI - Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 4
SP - [499]
EP - 506
AB - In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form $\Delta ^2y_{n-1}+q_ny_{\sigma (n)}^\gamma =g_n$, where $\gamma $ is a quotient of odd positive integers, in the superlinear case $(\gamma >1)$ and in the sublinear case $(\gamma <1)$.
LA - eng
KW - oscillation; nonlinear delay difference equation; Emden-Fowler type; oscillation; nonlinear delay difference equation; Emden-Fowler type
UR - http://eudml.org/doc/33443
ER -

References

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  1. Agarwal R. P., Difference Equations and Inequalities, Marcel Dekker, New York 1992 Zbl0952.39001MR1155840
  2. Gaef J. R., Spikes P. W., 10.1155/S0161171294000542, Internat. J. Math. Math. Sci. 17 (1994), 397–400 (1994) MR1261087DOI10.1155/S0161171294000542
  3. Gaef J. R., Spikes P. W., Asymptotic decay of oscillatory solutions of forced nonlinear difference equations, Dynamic Systems Appl. 3 (1994), 95–102 (1994) MR1261052
  4. Hooker J. W., 10.1080/10236199608808056, J. Differential Equations Appl. 2 (1996), 219–226 (1996) Zbl0856.34036MR1384571DOI10.1080/10236199608808056
  5. Hooker J. W., Patula W. T., 10.1016/0022-247X(83)90088-4, J. Math. Anal. Appl. 91 (1983), 9–29 (1983) Zbl0508.39005MR0688528DOI10.1016/0022-247X(83)90088-4
  6. Kordonis I. G. E., Philos, Ch. G., Purnaras I. K., 10.1016/S0377-0427(97)00126-X, J. Comput. Appl. Math. 84 (1997), 219–241 (1997) Zbl0885.39006MR1475376DOI10.1016/S0377-0427(97)00126-X
  7. Lakshmikantham V., Trigiante D., Theory of Difference Equations: Numerical Methods and Applications, Academic Press, New York 1988 Zbl1014.39001MR0939611
  8. Moore R. E., Computational Functional Analysis, (Ellis Harwood Series.) Halstred Press, New York 1985 Zbl1127.46001MR0783431
  9. Patula W. T., 10.1137/0510114, SIAM J. Math. Anal. 10 (1979), 1272–1279 (1979) MR0547812DOI10.1137/0510114
  10. Popenda J., On the oscillation of solutions of difference equations, Demonstratio Math. 28 (1995), 575–586 (1995) Zbl0846.39006MR1362187
  11. Szmanda B., 10.1016/0022-247X(85)90174-X, J. Math. Anal. Appl. 109 (1985), 22–30 (1985) Zbl0589.39003MR0796040DOI10.1016/0022-247X(85)90174-X
  12. Thandapani E., Pandian S., On the oscillatory behavior of solutions of second order nonlinear difference equation, Z. Anal. Anwendungen 13 (1993), 347–358 (1993) 
  13. Thandapani E., Ramuppillai L., 10.4171/ZAA/836, Z. Anal. Anwendungen 17 (1998), 1–10 (1998) Zbl0906.39008MR1632500DOI10.4171/ZAA/836
  14. Zafer A., On the existence of positive solutions and oscillation of solutions of higher order differenced equations with forcing terms, Comput. Math. Appl., to appear MR1666123
  15. Zhang B. G., 10.1006/jmaa.1993.1052, J. Math. Anal. Appl. 173 (1993), 58–68 (1993) Zbl0780.39006MR1205909DOI10.1006/jmaa.1993.1052

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