| 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 |
| . |
