Oscillation of third-order half-linear neutral difference equations

Ethiraju Thandapani; S. Selvarangam

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 1, page 87-104
  • ISSN: 0862-7959

Abstract

top
Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form Δ ( a n ( Δ 2 ( x n + b n x n - δ ) ) α ) + q n x n + 1 - τ α = 0 and Δ ( a n ( Δ 2 ( x n - b n x n - δ ) ) α ) + q n x n + 1 - τ α = 0 are established. Some examples are presented to illustrate the main results.

How to cite

top

Thandapani, Ethiraju, and Selvarangam, S.. "Oscillation of third-order half-linear neutral difference equations." Mathematica Bohemica 138.1 (2013): 87-104. <http://eudml.org/doc/252471>.

@article{Thandapani2013,
abstract = {Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form \begin\{equation*\} \Delta (a\_n(\Delta ^2(x\_n+b\_\{n\}x\_\{n-\delta \}))^\alpha )+q\_\{n\}x^\{\alpha \}\_\{n+1-\tau \}=0 \end\{equation*\} and \begin\{equation*\} \Delta (a\_n(\Delta ^2(x\_n-b\_nx\_\{n-\delta \}))^\alpha )+q\_nx^\{\alpha \}\_\{n+1-\tau \}=0 \end\{equation*\} are established. Some examples are presented to illustrate the main results.},
author = {Thandapani, Ethiraju, Selvarangam, S.},
journal = {Mathematica Bohemica},
keywords = {third order neutral difference equation; oscillation; nonoscillation; third-order neutral difference equation; oscillation; nonoscillation},
language = {eng},
number = {1},
pages = {87-104},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of third-order half-linear neutral difference equations},
url = {http://eudml.org/doc/252471},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Thandapani, Ethiraju
AU - Selvarangam, S.
TI - Oscillation of third-order half-linear neutral difference equations
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 1
SP - 87
EP - 104
AB - Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form \begin{equation*} \Delta (a_n(\Delta ^2(x_n+b_{n}x_{n-\delta }))^\alpha )+q_{n}x^{\alpha }_{n+1-\tau }=0 \end{equation*} and \begin{equation*} \Delta (a_n(\Delta ^2(x_n-b_nx_{n-\delta }))^\alpha )+q_nx^{\alpha }_{n+1-\tau }=0 \end{equation*} are established. Some examples are presented to illustrate the main results.
LA - eng
KW - third order neutral difference equation; oscillation; nonoscillation; third-order neutral difference equation; oscillation; nonoscillation
UR - http://eudml.org/doc/252471
ER -

References

top
  1. Agarwal, R. P., Difference Equations and Inequalities, 2nd edition, Marcel Dekker, New York (2000). (2000) Zbl0952.39001MR1740241
  2. Agarwal, R. P., Grace, S. R., O'Regan, D., Oscillation Theory for Difference and Functional Differential Equations, Kluwer, Dordrecht (2000). (2000) Zbl0954.34002
  3. Agarwal, R. P., Bohner, M., Grace, S. R., O'Regan, D., Discrete Oscillations Theory. Hindawi, New York, (2005). (2005) MR2179948
  4. Artzroumi, M., 10.1007/BF00276233, J. Math. Biology 21 (1985), 363-381. (1985) MR0804157DOI10.1007/BF00276233
  5. Baculíková, B., Džurina, J., 10.1016/j.mcm.2010.02.011, Math. Comput. Modelling 52 (2010), 215-226. (2010) MR2645933DOI10.1016/j.mcm.2010.02.011
  6. Arkin, Y. Bolat,&quot;{O}., 10.1016/j.aml.2004.07.011, Appl. Math. Lett. 17 (2004), 1073-1078. (2004) MR2087757DOI10.1016/j.aml.2004.07.011
  7. Chen, M. P., Lalli, B. S., Yu, J. S., 10.1016/0898-1221(94)00223-8, Computers Math Appl. 29 (1995), 5-11. (1995) Zbl0819.39004MR1326277DOI10.1016/0898-1221(94)00223-8
  8. Grace, S. R., Hamedani, G. G., On the oscillation of certain neutral difference equations, Math. Bohem. 125 (2000), 307-321. (2000) Zbl0969.39006MR1790122
  9. Graef, J. R., Miciano, A., Spikes, P. W., Sundaran, P., Thandapani, E., 10.1017/S0334270000000552, J. Aust. Math. Soc., Ser. B 38 (1996), 163-171. (1996) MR1414357DOI10.1017/S0334270000000552
  10. Lalli, B. S., Zhang, B. G., Li, J. Z., 10.1016/0022-247X(91)90278-8, J. Math. Anal. Appl. 158 (1991), 213-233. (1991) Zbl0732.39002MR1113411DOI10.1016/0022-247X(91)90278-8
  11. Lalli, B. S., Zhang, B. G., 10.1017/S0334270000008754, J. Aust. Math. Soc., Ser B 34 (1992), 245-256. (1992) Zbl0759.39002MR1181576DOI10.1017/S0334270000008754
  12. Lalli, B. S., 10.1016/0898-1221(94)00107-3, Comput. Math. Appl. 28 (1994), 191-202. (1994) Zbl0807.39004MR1284234DOI10.1016/0898-1221(94)00107-3
  13. Li, W. T., 10.1016/S0893-9659(98)00047-0, Appl. Math. Lett. 4 (1998), 1-8. (1998) Zbl0946.39002DOI10.1016/S0893-9659(98)00047-0
  14. Lin, X. Y., 10.1016/j.camwa.2005.05.003, Comp. Math. Appl. 50 (2005), 683-691. (2005) Zbl1089.39002MR2165630DOI10.1016/j.camwa.2005.05.003
  15. Saker, S. H., Oscillation and asymptotic behavior of third order neutral delay difference equations, Dym. Syst. Appl. 15 (2006), 549-568. (2006) MR2367663
  16. Sobiło, A. A., Migda, M., On the oscillation of solutions of third order linear difference equations of neutral type, Math. Bohem. 130 (2005), 19-33. (2005) Zbl1110.39002MR2128356
  17. Tang, X., Yan, J., Oscillation and nonoscillation of an odd order nonlinear difference equations, Funct. Differ. Equ. 7 (2000), 157-166. (2000) MR1941865
  18. Thandapani, E., Mahalingam, K., Oscillatory properties of third order neutral delay difference equations, Demon. Math. 35 (2002), 325-337. (2002) Zbl1034.39010MR1907305
  19. Zhou, Z., Oscillation for nonlinear difference equation of higher order, J. Math. Study 34 (2001), 282-286. (2001) MR1864910

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.