| Title:
|
Substitution method for generalized linear differential equations (English) |
| Author:
|
Fraňková, Dana |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
337-359 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The generalized linear differential equation $dx=d[a(t)]x+df$ where $A,f\in BV^{loc}_n(J)$ and the matrices $I-\Delta^-\ A(t), I+\Delta^+\ A(t)$ are regular, can be transformed $\frac{dy}{ds}=B(s)y+g(s)$ using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated. (English) |
| Keyword:
|
generalized linear differential equation |
| Keyword:
|
substitution method |
| Keyword:
|
variational stability |
| Keyword:
|
logarithmic prolongation |
| Keyword:
|
ordinary linear differential equation with a substitution |
| MSC:
|
34A30 |
| MSC:
|
34A99 |
| MSC:
|
34D05 |
| MSC:
|
34D99 |
| idZBL:
|
Zbl 0743.34023 |
| idMR:
|
MR1146392 |
| DOI:
|
10.21136/MB.1991.126028 |
| . |
| Date available:
|
2009-09-24T20:46:56Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126028 |
| . |
| Reference:
|
[F] Fraňková D.: A discontinuous substitution in the generalized Perron integral.(to appear in Mathematica Bohemica). |
| Reference:
|
[FS] Fraňková D., Schwabik Š.: Generalized Sturm-Liouville equations II.Czechoslovak Math. J. 38 (113) 1988, 531-553. MR 0950307 |
| Reference:
|
[K] Kurzweil J.: Ordinary differential equations.Studies in Applied Mechanics 13. Elsevier Amsterdam-Oxford-New York-Tokyo 1986. Zbl 0667.34002, MR 0929466 |
| Reference:
|
[S1] Schwabik Š.: Generalized differential equations. Fundamental results.Rozpravy ČSAV, Academia Praha 1985. Zbl 0594.34002, MR 0823224 |
| Reference:
|
[S2] Schwabik Š.: Variational stability for generalized ordinary differential equations.Časopis pěst. mat. 109 (1984), Praha, 389-420. Zbl 0574.34034, MR 0774281 |
| Reference:
|
[STV] Schwabik Š., Tvrdý M., Vejvoda O.: Differential and integral equations. Boundary Value Problems and Adjoints.Academia Praha, Reidel Dordrecht, 1979. MR 0542283 |
| . |
