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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:
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


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