# Article

 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: http://hdl.handle.net/10338.dmlcz/127739 . 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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