| Title:
|
The oscillation of an $m$th order perturbed nonlinear difference equation (English) |
| Author:
|
Wong, P. J. Y. |
| Author:
|
Agarwal, Ravi P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
13-27 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We offer sufficient conditions for the oscillation of all solutions of the perturbed difference equation $$|\Delta^{m} y(k)|^{\alpha-1}\Delta^{m} y(k)+Q(k,y(k-\sigma_{k}), \Delta y(k-\sigma_{k}),\cdots, \Delta^{m-2}y(k-\sigma_{k}))$$ \hfill $=P(k,y(k-\sigma_{k}),\Delta y(k-\sigma_{k}),\cdots, \Delta^{m-1}y(k-\sigma_{k})),~k\geq k_{0}$ where $\alpha>0.$ Examples which dwell upon the importance of our results are also included. (English) |
| Keyword:
|
oscillatory solutions |
| Keyword:
|
difference equations |
| MSC:
|
39A10 |
| idZBL:
|
Zbl 0870.39001 |
| idMR:
|
MR1399838 |
| . |
| Date available:
|
2008-06-06T21:29:57Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107559 |
| . |
| Reference:
|
[1] Agarwal R. P.: Difference Equations and Inequalities.Marcel Dekker, New York, 1992. Zbl 0925.39001, MR 1155840 |
| Reference:
|
[2] Agarwal R. P.: Properties of solutions of higher order nonlinear difference equations I.An. St. Univ. Iasi 29(1983), 85-96. MR 0739573 |
| Reference:
|
[3] Agarwal R. P.: Difference calculus with applications to difference equations.in General Inequalities, ed. W. Walter, ISNM 71, Birkhaver Verlag, Basel (1984), 95-160. Zbl 0592.39001, MR 0821789 |
| Reference:
|
[4] Agarwal R. P.: Properties of solutions of higher order nonlinear difference equations II.An. St. Univ. Iasi 29(1985), 165-172. MR 0858057 |
| Reference:
|
[5] Grace S. R., Lalli B. S.: Oscillation theorems for $n$th order delay equations.J. Math. Anal. Appl. 91(1983), 342-366. MR 0690876 |
| Reference:
|
[6] Grace S. R., Lalli B. S.: Oscillation theorems for damped differential equations of even order with deviating arguments.SIAM J. Math. Anal. 15(1984), 308-316. Zbl 0542.34057, MR 0731869 |
| Reference:
|
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| Reference:
|
[8] Lakshmikantham V., Trigiante D.: Difference Equations with Applications to Numerical Analysis.Academic Press, New York, 1988. MR 0939611 |
| Reference:
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[9] Popenda J. : Oscillation and nonoscillation theorems for second order difference equations.J. Math. Anal. Appl. 123(1987), 34-38. Zbl 0612.39002, MR 0881528 |
| Reference:
|
[10] Staikos V. A.: Basic results on oscillation for differential equations.Hiroshima Math. J. 10(1980), 495-516. Zbl 0453.34055, MR 0594131 |
| Reference:
|
[11] Thandapani E.: Oscillatory behavior of solutions of second order nonlinear difference equations.J. Math. Phys. Sci. 25(1991), 451-464. |
| Reference:
|
[12] Thandapani E., Sundaram P.: Oscillation theorems for some even order nonlinear difference equations.preprint. |
| Reference:
|
[13] Wong P. J. Y., Agarwal R. P.: Oscillation theorems and existence of positive monotone solutions for second order nonlinear difference equations.Math. Comp. Modelling 21(1995), 63-84. Zbl 0820.39002, MR 1316120 |
| Reference:
|
[14] Wong P. J. Y., Agarwal R. P.: Oscillation theorems and existence criteria of asymptotically monotone solutions for second order differential equations.Dynamic Systems and Applications, to appear. Zbl 0840.34021, MR 1365834 |
| Reference:
|
[15] Wong P. J. Y., Agarwal R. P.: Oscillatory behavior of solutions of certain second order nonlinear differential equations.J. Math. Anal. Applic., 198 (1996), 337-354. MR 1376268 |
| Reference:
|
[16] Wong P. J. Y., Agarwal R. P.: Oscillation theorems for certain second order nonlinear difference equations.to appear. Zbl 0874.39012, MR 1422774 |
| Reference:
|
[17] Wong P. J. Y., Agarwal R. P.: Oscillation and monotone solutions of a second order quasilinear difference equation.to appear. |
| Reference:
|
[18] Wong P. J. Y., Agarwal R. P.: On the oscillation and asymptotically monotone solutions of second order quasilinear differential equations.Appl. Math. Comp., to appear. MR 1407599 |
| Reference:
|
[19] Wong P. J. Y., Agarwal R. P.: Oscillations and nonoscillations of half-linear difference equations generated by deviating arguments, Advances in Difference Equations II.Computers Math. Applic., to appear. MR 1666122 |
| Reference:
|
[20] Wong Z., Yu J.: Oscillation criteria for second order nonlinear difference equations.Funk. Ekv. 34(1991), 313-319. |
| . |
