| Title:
|
New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations (English) |
| Author:
|
Hakl, R. |
| Author:
|
Lomtatidze, A. |
| Author:
|
Půža, B. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
509-524 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The nonimprovable sufficient conditions for 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, $q\in L(I;\mathbb{R})$, $c\in \mathbb{R}$, are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator $\ell $ is not of Volterra’s type with respect to the point $a$. (English) |
| Keyword:
|
linear functional differential equations |
| Keyword:
|
differential equations with deviating arguments |
| Keyword:
|
initial value problems |
| MSC:
|
34K05 |
| MSC:
|
34K06 |
| MSC:
|
34K10 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 1017.34065 |
| idMR:
|
MR1942637 |
| DOI:
|
10.21136/MB.2002.133950 |
| . |
| Date available:
|
2009-09-24T22:04:31Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133950 |
| . |
| Reference:
|
[1] Azbelev, N. V.; Maksimov, V. P.; Rakhmatullina, L. F.: Introduction to the Theory of Functional Differential Equations.Nauka, Moskva, 1991. (Russian) MR 1144998 |
| Reference:
|
[2] Bravyi, E.; Hakl, R.; Lomtatidze, A.: Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations.Czechoslovak Math. J (to appear). MR 1923257 |
| Reference:
|
[3] Bravyi, E.: A note on the Fredholm property of boundary value problems for linear functional differential equations.Mem. Differential Equations Math. Phys. 20 (2000), 133–135. Zbl 0968.34049, MR 1789344 |
| Reference:
|
[4] Gelashvili, Sh.; Kiguradze, I.: 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:
|
[5] Kiguradze, I.; Půža, B.: 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:
|
[6] Schwabik, Š.; Tvrdý, M.; Vejvoda, O.: Differential and Integral Equations: Boundary Value Problems and Adjoints.Academia, Praha, 1979. MR 0542283 |
| . |
