| Title:
|
Transformations $z(t)=L(t)y(\varphi(t))$ of ordinary differential equations (English) |
| Author:
|
Tryhuk, Václav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
519-529 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper describes the general form of an ordinary differential equation of an order $n+1$ $(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form \[ f\biggl (s, w_{00}v_0, \ldots , \sum _{j=0}^n w_{n j}v_j\biggr )=\sum _{j=0}^n w_{n+1 j}v_j + w_{n+1 n+1}f(x,v, v_1, \ldots , v_n), \] where $w_{n+1 0}=h(s, x, x_1, u, u_1, \ldots , u_n)$, $ w_{n+1 1}=g(s, x, x_1, \ldots , x_n, u, u_1, \ldots , u_n)$ and $w_{i j}=a_{i j}(x_1, \ldots , x_{i-j+1}, u, u_1, \ldots , u_{i-j})$ for the given functions $a_{i j}$ is solved on $\mathbb R$, $ u\ne 0.$ (English) |
| Keyword:
|
ordinary differential equations |
| Keyword:
|
linear differential equations |
| Keyword:
|
transformations |
| Keyword:
|
functional equations |
| MSC:
|
34A25 |
| MSC:
|
34A30 |
| MSC:
|
34A34 |
| MSC:
|
39B22 |
| MSC:
|
39B40 |
| idZBL:
|
Zbl 1079.34506 |
| idMR:
|
MR1777473 |
| . |
| Date available:
|
2009-09-24T10:35:12Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127589 |
| . |
| Reference:
|
[n1] J. Aczél: Lectures on Functional Equations and Their Applications.Academic Press, New York, 1966. MR 0208210 |
| Reference:
|
[n2] J. Aczél: Über Zusammenhänge zwischen Differential- und Funktionalgleichungen.Jahresber. Deutsch. Math.-Verein. 71 (1969), 55–57. MR 0256014 |
| Reference:
|
[n3] O. Borůvka: Linear Differential Transformations of the Second Order.The English Univ. Press, London, 1971. MR 0463539 |
| Reference:
|
[n4] A. Moór, L. Pintér: Untersuchungen Über den Zusammenhang von Differential- und Funktionalgleichungen.Publ. Math. Debrecen 13 (1966), 207–223. MR 0206445 |
| Reference:
|
[n5] F. Neuman: 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:
|
[n6] J. Posluszny, L. A. Rubel: The motion of an ordinary differential equation.J. Differential Equations 34 (1979), 291–302. MR 0550047, 10.1016/0022-0396(79)90011-1 |
| Reference:
|
[n7] V. Tryhuk: On transformations $z(t)=y(\varphi (t))$ of ordinary differential equations.Czechoslovak Math. J. 50 (125) (2000), 509–518. Zbl 1079.34505, MR 1777472, 10.1023/A:1022877409091 |
| Reference:
|
[n8] V. Tryhuk: On global transformations of ordinary differential equations of the second order.Czechoslovak Math. J. 50 (125) (2000), 499–508. Zbl 1079.34502, MR 1777471, 10.1023/A:1022825325021 |
| Reference:
|
[n9] V. Tryhuk: Remark to transformations of linear differential and functional-differential equations.Czechoslovak Math. J. 50 (125) (2000), 265–278. MR 1761386, 10.1023/A:1022414717364 |
| . |
