| Title:
|
Asymptotic estimation for functional differential equations with several delays (English) |
| Author:
|
Čermák, Jan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
337-345 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss the asymptotic behaviour of all solutions of the functional differential equation \[y^{\prime }(x)=\sum _{i=1}^ma_i(x)y(\tau _i(x))+b(x)y(x)\,,\] where $b(x)<0$. The asymptotic bounds are given in terms of a solution of the functional nondifferential equation \[\sum _{i=1}^m|a_i(x)|\omega (\tau _i(x))+b(x)\omega (x)=0.\] (English) |
| Keyword:
|
functional differential equation |
| Keyword:
|
functional nondifferential equation |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
transformation |
| MSC:
|
34K25 |
| MSC:
|
39B99 |
| idZBL:
|
Zbl 1048.34126 |
| idMR:
|
MR1744521 |
| . |
| Date available:
|
2008-06-06T22:24:50Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107708 |
| . |
| Reference:
|
[1] Čermák, J.: On the asymptotic behaviour of solutions of certain functional differential equations.Math. Slovaca 48 (1998), 187–212. MR 1647674 |
| Reference:
|
[2] Čermák, J.: The asymptotic bounds of linear delay systems.J. Math. Anal. Appl. 225 (1998), 373–388. MR 1644331 |
| Reference:
|
[3] Dibl¡k, J.: Asymptotic equilibrium for a class of delay differential equations.Proc. of the Second International Conference on Difference Equations, S. Elaydi, I. Győri, G. Ladas (eds.), 1995, pp. 137–143. MR 1636319 |
| Reference:
|
[4] Hale, J. K., Verduyn Lunel, S. M.: Introduction to Functional Differential Equations, Springer-Verlag.New York, 1993. MR 1243878 |
| Reference:
|
[5] Heard, M. L.: A change of variables for functional differential equations.J. Differential Equations 18 (1975), 1–10. Zbl 0318.34069, MR 0387766 |
| Reference:
|
[6] Kato, T., Mcleod, J. B.: The functional differential equation $y^{\prime }(x)=ay(\lambda x)+by(x)$.Bull. Amer. Math. Soc. 77 (1971), 891–397. MR 0283338 |
| Reference:
|
[7] Kuczma, M., Choczewski, B., Ger, R.: Iterative Functional Equations, Encyclopedia of Mathematics and its Applications.Cambridge University Press, 1990. MR 1067720 |
| Reference:
|
[8] Neuman, F.: Simultaneous solutions of a system of Abel equations and differential equations with several deviations.Czechoslovak Math. J. 32 (107) (1982), 488–494. Zbl 0524.34070, MR 0669790 |
| Reference:
|
[9] Neuman, F.: Transformations and canonical forms of functional-differential equations.Proc. Roy. Soc. Edinburgh 115A (1990), 349–357. MR 1069527 |
| Reference:
|
[10] Zdun, M.: On Simultaneous Abel equations.Aequationes Math. (1989), 163–177. Zbl 0686.39009, MR 1018910 |
| . |
