| Title:
|
On global transformations of functional-differential equations of the first order (English) |
| Author:
|
Tryhuk, Václav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
279-293 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper describes the general form of functional-differential equations of the first order with $m (m\ge 1)$ delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation \[ f(t, uv, u_{1}v_{1}, \ldots , u_{m}v_{m}) = f(x, v, v_{1}, \ldots , v_{m})g(t, x, u, u_{1}, \ldots , u_{m})u + h(t, x, u, u_{1}, \ldots , u_{m})v \] for $u\ne 0$ is solved on $\mathbb R$ and a method of proof by J. Aczél is applied. (English) |
| Keyword:
|
functional differential equations |
| Keyword:
|
ordinary differential equations |
| Keyword:
|
global transformations |
| Keyword:
|
functional equations in a single variable |
| Keyword:
|
functional equations in several variables |
| MSC:
|
34-02 |
| MSC:
|
34C20 |
| MSC:
|
34K05 |
| MSC:
|
34K15 |
| MSC:
|
39B40 |
| idZBL:
|
Zbl 1054.34105 |
| idMR:
|
MR1761387 |
| . |
| Date available:
|
2009-09-24T10:32:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127569 |
| . |
| Reference:
|
[n1] Aczél, J.: Über Zusammenhänge zwischen Differential- und Funktionalgleichungen.Jahresber. Deutsch. Math.-Verein. 71 (1969), 55–57. MR 0256014 |
| Reference:
|
[n3] Aczél, J.: Lectures on Functional Equations and Their Applications.Academic Press, New York, 1966. MR 0208210 |
| Reference:
|
[n4] Čermák, J.: Continuous transformations of differential equations with delays.Georgian Math. J. 2 (1995), 1–8. MR 1310496, 10.1007/BF02257729 |
| Reference:
|
[n5] Ladde, G.S., Lakshmikantham, V., Zhang, B.G.: Oscillation Theory of Differential Equations with Deviating Arguments.Marcel Dekker, New York and Basel, 1987. MR 1017244 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[n8] Neuman, F.: Transformations and canonical forms of functional-differential equations.Proc. Roy. Soc. Edinburgh 115 A (1990), 349–357. MR 1069527 |
| Reference:
|
[n9] Neuman, F.: Global Properties of Linear Ordinary Differential Equations.Mathematics and Its Applications (East European Series) 52, Kluwer Acad. Publ., Dordrecht-Boston-London, 1991. Zbl 0784.34009, MR 1192133 |
| Reference:
|
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| Reference:
|
[n11] Tryhuk, V.: The most general transformations of homogeneous linear differential retarded equations of the first order.Arch. Math. (Brno) 16 (1980), 225–230. MR 0594470 |
| Reference:
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| Reference:
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| Reference:
|
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| . |
