| Title:
|
On the oscillation of Volterra summation equations (English) |
| Author:
|
Thandapani, E. |
| Author:
|
Ravi, K. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
41-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The asymptotic and oscillatory behavior of solutions of Volterra summation equations \[ y_{n}=p_{n} \pm \sum _{s=0}^{n-1}K(n,s)f(s,y_{s}), \ n\in \mathbb{N} \] where $\mathbb{N}=\lbrace 0,1,2,\dots \rbrace $, are studied. Examples are included to illustrate the results. (English) |
| Keyword:
|
Volterra summation equations |
| Keyword:
|
oscillation |
| Keyword:
|
asymptotic behavior |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 0982.39005 |
| idMR:
|
MR1825856 |
| DOI:
|
10.21136/MB.2001.133922 |
| . |
| Date available:
|
2009-09-24T21:47:02Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133922 |
| . |
| Reference:
|
[1] R. P. Agarwal: Difference Equations and Inequalities.Marcel Dekker, New York, 1992. Zbl 0925.39001, MR 1155840 |
| Reference:
|
[2] R. P. Agarwal, P. J. Y. Wong: Advanced Topics in Diffference Equations.Kluwer Publ., Dordrecht, 1997. MR 1447437 |
| Reference:
|
[3] J. R. Graef, E. Thandapani: Oscillatory behavior of solutions of Volterra summation equations.Appl. Math. Lett (to appear). MR 1750064 |
| Reference:
|
[4] V. L. Kocic, G. Ladas: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications.Kluwer Publ., Dordrecht, 1993. MR 1247956 |
| Reference:
|
[5] S. N. Elaydi: Periodicity and stability of linear Volterra difference systems.(to appear). MR 1260872 |
| Reference:
|
[6] S. N. Elaydi, V. L. Kocic: Global stability of a nonlinear Volterra difference systems.Diff. Equations Dynam. Systems 2 (1994), 337–345. MR 1386278 |
| Reference:
|
[7] E. Thandapani, B. S. Lalli: Asymptotic behavior and oscillations of a difference equations of Volterra type.Appl. Math. Lett. 7 (1994), 89–93. MR 1349901, 10.1016/0893-9659(94)90060-4 |
| Reference:
|
[8] V. Lakshmikantham, D. Trigiante: Theory of Difference Equations.Academic Press, New York, 1988. MR 0939611 |
| Reference:
|
[9] O. Akinyele: Asymptotic properties of solutions of a Volterra integral equations with delay.An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 30 (1984), 25–30. MR 0800137 |
| . |
