| Title:
|
On global transformations of ordinary differential equations of the second order (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:
|
499-508 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper describes the general form of an ordinary differential equation of the second order 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 \[ f(t,vy,wy+uvz)=f(x,y,z)u^{2}v+g(t,x,u,v,w)vz+h(t,x,u,v,w)y+2uwz \] is solved on $\mathbb R$ for $y\ne 0$, $v\ne 0.$ (English) |
| Keyword:
|
ordinary differential equations |
| Keyword:
|
linear differential equations |
| Keyword:
|
global transformations |
| Keyword:
|
functional equations |
| MSC:
|
34-02 |
| MSC:
|
34A25 |
| MSC:
|
34A30 |
| MSC:
|
34A34 |
| MSC:
|
34C20 |
| MSC:
|
39-02 |
| MSC:
|
39B22 |
| MSC:
|
39B40 |
| idZBL:
|
Zbl 1079.34502 |
| idMR:
|
MR1777471 |
| . |
| Date available:
|
2009-09-24T10:34:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127587 |
| . |
| Reference:
|
[n1] J. Aczél: Über Zusammenhänge zwischen Differential- und Funktionalgleichungen.Jahresber. Deutsch. Math.-Verein. 71 (1969), 55–57. MR 0256014 |
| Reference:
|
[n3] J. Aczél: Lectures on Functional Equations and Their Applications.Academic Press, New York, 1966. MR 0208210 |
| Reference:
|
[n4] M. Čadek: Form of general pointwise transformations of linear differential equations.Czechoslovak Math. J. 35 (110) (1985), 617–624. MR 0809044 |
| Reference:
|
[n5] M. Čadek: Pointwise transformations of linear differential equations.Arch. Math. (Brno) 26 (1990), 187–200. MR 1188970 |
| Reference:
|
[n2] A. Moór, L. Pintér: Untersuchungen Über den Zusammenhang von Differential- und Funktionalgleichungen.Publ. Math. Debrecen 13 (1966), 207–223. MR 0206445 |
| Reference:
|
[n6] 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:
|
[n7] F. Neuman: A note on smoothness of the Stäckel transformation.Prace Math. WSP Krakow 11 (1985), 147–151. |
| Reference:
|
[n8] P. Stäckel: Über Transformationen von Differentialgleichungen.J. Reine Angew. Math. (Crelle Journal) 111 (1893), 290–302. |
| Reference:
|
[n9] E. J. Wilczynski: Projective differential geometry of curves and ruled spaces.Teubner, Leipzig, 1906. |
| . |
