| Title:
|
A note on the Cauchy problem for first order linear differential equations with a deviating argument (English) |
| Author:
|
Hakl, Robert |
| Author:
|
Lomtatidze, Alexander |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
61-71 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Conditions for the existence and uniqueness of a solution of the Cauchy problem \[ u^{\prime }(t)=p(t)u(\tau (t))+q(t)\,,\qquad u(a)=c\,, \] established in [2], are formulated more precisely and refined for the special case, where the function $\tau $ maps the interval $]a,b[$ into some subinterval $[\tau _0,\tau _1]\subseteq [a,b]$, which can be degenerated to a point. (English) |
| Keyword:
|
first order equation |
| Keyword:
|
differential equation with deviating arguments |
| Keyword:
|
initial value problems |
| MSC:
|
34K06 |
| idZBL:
|
Zbl 1087.34043 |
| idMR:
|
MR1899569 |
| . |
| Date available:
|
2008-06-06T22:29:53Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107820 |
| . |
| Reference:
|
[1] 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:
|
[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. Zbl 1023.34055, MR 1923257 |
| Reference:
|
[3] Hakl R., Lomtatidze A., Půža B.: New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations.Math. Bohem., to appear. Zbl 1017.34065, MR 1942637 |
| Reference:
|
[4] Kiguradze I., Půža B.: On boundary value problems for systems of linear functional differential equations.Czechoslovak Math. J. 47 (1997), No. 2, 341–373. Zbl 0930.34047, MR 1452425 |
| . |
