| Title:
|
On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type (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:
|
4 |
| Year:
|
2002 |
| Pages:
|
673-690 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
On the segment $I=[a,b]$ consider the problem \[ u^{\prime }(t)=f(u)(t) , \quad u(a)=c, \] where $f\:C(I,\mathbb{R})\rightarrow L(I,\mathbb{R})$ is a continuous, in general nonlinear operator satisfying Carathéodory condition, and $c\in \mathbb{R}$. The effective sufficient conditions guaranteeing the solvability and unique solvability of the considered problem are established. Examples verifying the optimality of obtained results are given, as well. (English) |
| Keyword:
|
nonlinear functional differential equation |
| Keyword:
|
initial value problem |
| Keyword:
|
non–Volterra’s type operator |
| MSC:
|
34K05 |
| MSC:
|
34K10 |
| MSC:
|
34K99 |
| idZBL:
|
Zbl 1023.34054 |
| idMR:
|
MR1940049 |
| . |
| Date available:
|
2009-09-24T10:55:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127754 |
| . |
| Reference:
|
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| . |
