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Title: Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations (English)
Author: Bravyi, E.
Author: Hakl, R.
Author: Lomtatidze, A.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 52
Issue: 3
Year: 2002
Pages: 513-530
Summary lang: English
Category: math
Summary: Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t), \qquad u(a)=c, \] where $\ell \:C(I,\mathbb R)\rightarrow L(I,\mathbb R)$ is a linear bounded operator, $q\in L(I,\mathbb R)$, and $c\in \mathbb R$, are established. (English)
Keyword: linear functional differential equations
Keyword: Cauchy problem
Keyword: existence and uniqueness
Keyword: differential inequalities
MSC: 34K06
MSC: 34K10
idZBL: Zbl 1023.34055
idMR: MR1923257
Date available: 2009-09-24T10:53:37Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] N. V.  Azbelev, V. P.  Maksimov and L. F.  Rakhmatullina: Introduction to the Theory of Functional Differential Equations.Nauka, Moscow, 1991. (Russian) MR 1144998
Reference: [2] Sh.  Gelashvili and I.  Kiguradze: On multi-point boundary value problems for systems of functional differential and difference equations.Mem. Differential Equations Math. Phys. 5 (1995), 1–113. MR 1415806
Reference: [3] P.  Hartman: Ordinary Differential Equations.John Wiley, New York, 1964. Zbl 0125.32102, MR 0171038
Reference: [4] I.  Kiguradze and B.  Půža: On boundary value problems for systems of linear functional differential equations.Czechoslovak Math. J. 47 (1997), 341–373. MR 1452425, 10.1023/A:1022829931363
Reference: [5] Š.  Schwabik, M.  Tvrdý and O.  Vejvoda: Differential and integral equations: boundary value problems and adjoints.Academia, Praha, 1979. MR 0542283


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