| Title:
|
Oscillation properties for a scalar linear difference equation of mixed type (English) |
| Author:
|
Berezansky, Leonid |
| Author:
|
Pinelas, Sandra |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
169-182 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type $$ \Delta x(n)+\sum _{k=-p}^{q}a_{k}(n)x(n+k)=0,\quad n>n_{0}, $$ where $\Delta x(n)=x(n+1)-x(n)$ is the difference operator and $\{a_{k}(n)\}$ are sequences of real numbers for $k=-p,\ldots ,q$, and $p>0$, $q\geq 0$. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
difference equation |
| Keyword:
|
mixed type |
| Keyword:
|
asymptotic behavior |
| MSC:
|
39A21 |
| MSC:
|
39A99 |
| idZBL:
|
Zbl 06587861 |
| idMR:
|
MR3499783 |
| DOI:
|
10.21136/MB.2016.14 |
| . |
| Date available:
|
2016-05-19T09:04:52Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145711 |
| . |
| Reference:
|
[1] Agarwal, R. P.: Difference Equations and Inequalities: Theory, Methods, and Applications.Pure and Applied Mathematics 228 Marcel Dekker, New York (2000). Zbl 0952.39001, MR 1740241 |
| Reference:
|
[2] Asada, T., Yoshida, H.: Stability, instability and complex behavior in macrodynamic models with policy lag.Discrete Dyn. Nat. Soc. 5 (2001), 281-295. Zbl 0980.34070, 10.1155/S1026022600000583 |
| Reference:
|
[3] Berezansky, L., Braverman, E.: Some oscillation problems for a second order linear delay differential equation.J. Math. Anal. Appl. 220 (1998), 719-740. Zbl 0915.34064, MR 1614948, 10.1006/jmaa.1997.5879 |
| Reference:
|
[4] k, J. Diblí, Janglajew, K., ková, M. Kúdelčí: An explicit coefficient criterion for the existence of positive solutions to the linear advanced equation.Discrete Contin. Dyn. Syst. Ser. B 19 (2014), 2461-2467. MR 3275005, 10.3934/dcdsb.2014.19.2461 |
| Reference:
|
[5] k, J. Diblí, ková, M. Kúdelčí: New explicit integral criteria for the existence of positive solutions to the linear advanced equation $y'=c(t)y(t+\tau)$.Appl. Math. Lett. 38 (2014), 144-148. MR 3258218, 10.1016/j.aml.2014.06.020 |
| Reference:
|
[6] Dubois, D., Stecke, K. E.: Dynamic analysis of repetitive decision-free discrete-event processes: applications to production systems.Ann. Oper. Res. 26 (1990), 323-347. MR 1087827, 10.1007/BF02248590 |
| Reference:
|
[7] Ferreira, J. M., Pinelas, S.: Oscillatory mixed difference systems.Adv. Difference Equ. (2006), 1-18. Zbl 1139.39011, MR 2238984 |
| Reference:
|
[8] Frisch, R., Holme, H.: The characteristic solutions of a mixed difference and differential equation occurring in economic dynamics.Econometrica 3 (1935), 225-239. 10.2307/1907258 |
| Reference:
|
[9] Gandolfo, G.: Economic Dynamics.Berlin Springer (2010). Zbl 1177.91094, MR 2841165 |
| Reference:
|
[10] Iakovleva, V., Vanegas, C. J.: On the solution of differential equations with delayed and advanced arguments.Electron. J. Differ. Equ. 13 (2005), 57-63. Zbl 1092.34549, MR 2312906 |
| Reference:
|
[11] James, R. W., Belz, M. H.: The significance of the characteristic solutions of mixed difference and differential equations.Econometrica 6 (1938), 326-343. 10.2307/1905410 |
| Reference:
|
[12] Krisztin, T.: Nonoscillation for functional differential equations of mixed type.J. Math. Anal. Appl. 245 (2000), 326-345. Zbl 0955.34054, MR 1758543, 10.1006/jmaa.2000.6735 |
| Reference:
|
[13] Ladde, G. S., Lakshmikantham, V., Zhang, B. G.: Oscillation Theory of Differential Equations with Deviating Arguments.Pure and Applied Mathematics 110 Marcel Dekker, New York (1987). Zbl 0832.34071, MR 1017244 |
| Reference:
|
[14] Rogovchenko, Y. V.: Oscillation criteria for certain nonlinear differential equations.J. Math. Anal. Appl. 229 (1999), 399-416. Zbl 0921.34034, MR 1666412, 10.1006/jmaa.1998.6148 |
| . |
