Substitution method for generalized linear differential equations

Dana Fraňková

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 4, page 337-359
  • ISSN: 0862-7959

Abstract

top
The generalized linear differential equation d x = d [ a ( t ) ] x + d f where A , f B V n l o c ( J ) and the matrices I - Δ - A ( t ) , I + Δ + A ( t ) are regular, can be transformed d y d s = 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.

How to cite

top

Fraňková, 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
  1. Fraňková D., A discontinuous substitution in the generalized Perron integral, (to appear in Mathematica Bohemica). 
  2. Fraňková D., Schwabik Š., Generalized Sturm-Liouville equations II, Czechoslovak Math. J. 38 (113) 1988, 531-553. (1988) MR0950307
  3. Kurzweil J., Ordinary differential equations, Studies in Applied Mechanics 13. Elsevier Amsterdam-Oxford-New York-Tokyo 1986. (1986) Zbl0667.34002MR0929466
  4. Schwabik Š., Generalized differential equations. Fundamental results, Rozpravy ČSAV, Academia Praha 1985. (1985) Zbl0594.34002MR0823224
  5. Schwabik Š., Variational stability for generalized ordinary differential equations, Časopis pěst. mat. 109 (1984), Praha, 389-420. (1984) Zbl0574.34034MR0774281
  6. Schwabik Š., Tvrdý M., Vejvoda O., Differential and integral equations. Boundary Value Problems and Adjoints, Academia Praha, Reidel Dordrecht, 1979. (1979) MR0542283

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.