Substitution method for generalized linear differential equations
Mathematica Bohemica (1991)
- Volume: 116, Issue: 4, page 337-359
- ISSN: 0862-7959
Access Full Article
topAbstract
topHow to cite
topFraňková, Dana. "Substitution method for generalized linear differential equations." Mathematica Bohemica 116.4 (1991): 337-359. <http://eudml.org/doc/29182>.
@article{Fraňková1991,
abstract = {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.},
author = {Fraňková, Dana},
journal = {Mathematica Bohemica},
keywords = {generalized linear differential equation; substitution method; variational stability; logarithmic prolongation; ordinary linear differential equation with a substitution; generalized linear differential equation; substitution method; variational stability},
language = {eng},
number = {4},
pages = {337-359},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Substitution method for generalized linear differential equations},
url = {http://eudml.org/doc/29182},
volume = {116},
year = {1991},
}
TY - JOUR
AU - Fraňková, Dana
TI - Substitution method for generalized linear differential equations
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 4
SP - 337
EP - 359
AB - 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.
LA - eng
KW - generalized linear differential equation; substitution method; variational stability; logarithmic prolongation; ordinary linear differential equation with a substitution; generalized linear differential equation; substitution method; variational stability
UR - http://eudml.org/doc/29182
ER -
References
top- Fraňková D., A discontinuous substitution in the generalized Perron integral, (to appear in Mathematica Bohemica).
- Fraňková D., Schwabik Š., Generalized Sturm-Liouville equations II, Czechoslovak Math. J. 38 (113) 1988, 531-553. (1988) MR0950307
- Kurzweil J., Ordinary differential equations, Studies in Applied Mechanics 13. Elsevier Amsterdam-Oxford-New York-Tokyo 1986. (1986) Zbl0667.34002MR0929466
- Schwabik Š., Generalized differential equations. Fundamental results, Rozpravy ČSAV, Academia Praha 1985. (1985) Zbl0594.34002MR0823224
- Schwabik Š., Variational stability for generalized ordinary differential equations, Časopis pěst. mat. 109 (1984), Praha, 389-420. (1984) Zbl0574.34034MR0774281
- Schwabik Š., Tvrdý M., Vejvoda O., Differential and integral equations. Boundary Value Problems and Adjoints, Academia Praha, Reidel Dordrecht, 1979. (1979) MR0542283
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.