| Title:
|
Asymptotic properties of differential equations with advanced argument (English) |
| Author:
|
Čermák, Jan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
825-837 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation \[ y^{\prime }(x)=ay(\tau (x))+by(x),\qquad x\in [x_0,\infty ) \] of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution $y(x)$ which behaves in this way. (English) |
| Keyword:
|
functional differential equation |
| Keyword:
|
functional (nondifferential) equation |
| Keyword:
|
advanced argument |
| Keyword:
|
asymptotic behaviour |
| MSC:
|
34K15 |
| MSC:
|
34K25 |
| MSC:
|
39B22 |
| idZBL:
|
Zbl 1079.34544 |
| idMR:
|
MR1792972 |
| . |
| Date available:
|
2009-09-24T10:38:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127612 |
| . |
| Reference:
|
[1] J. Čermák: The asymptotic bounds of linear delay systems.J. Math. Anal. Appl. 225 (1998), 373–388. MR 1644331, 10.1006/jmaa.1998.6018 |
| Reference:
|
[2] J. Diblík: Asymptotic representation of solutions of equation $\dot{y}(t)=\beta (t)[y(t)-y(t-\tau (t))]$.J. Math. Anal. Appl. 217 (1998), 200–215. MR 1492085, 10.1006/jmaa.1997.5709 |
| Reference:
|
[3] J. K. Hale and S. M. Verduyn Lunel: Functional Differential Equations.Springer-Verlag, New York, 1993. |
| Reference:
|
[4] M. L. Heard: Asymptotic behavior of solutions of the functional differential equation $x^{\prime }(t)=ax(t)+bx(t^{\alpha })$, $\alpha >1$.J. Math. Anal. Appl. 44 (1973), 745–757. Zbl 0289.34115, MR 0333405, 10.1016/0022-247X(73)90013-9 |
| Reference:
|
[5] M. L. Heard: A change of variables for functional differential equations.J. Differential Equations 18 (1975), 1–10. Zbl 0318.34069, MR 0387766, 10.1016/0022-0396(75)90076-5 |
| Reference:
|
[6] T. Kato and J. B. Mcleod: The functional differential equation $y^{\prime }(x)=ay(\lambda x)+by(x)$.Bull. Amer. Math. Soc. 77 (1971), 891–937. MR 0283338 |
| Reference:
|
[7] M. Kuczma, B. Choczewski and R. Ger: Iterative Functional Equations.Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1990. MR 1067720 |
| Reference:
|
[8] G. S. Ladde, V. Lakshmikantham and B. G. Zhang: Oscillation Theory of Differential Equations with Deviating Argument.Marcel Dekker, Inc., New York, 1987. MR 1017244 |
| Reference:
|
[9] F. Neuman: On transformations of differential equations and systems with deviating argument.Czechoslovak Math. J. 31(106) (1981), 87–90. Zbl 0463.34051, MR 0604115 |
| Reference:
|
[10] F. Neuman: Transformations and canonical forms of functional-differential equations.Proc. Roy. Soc. Edinburgh 115A (1990), 349–357. MR 1069527 |
| Reference:
|
[11] V. A. Staikos and P. Ch. Tsamatos: On the terminal value problem for differential equations with deviating arguments.Arch. Math. (Brno) (1985), 43–49. MR 0818306 |
| . |
