| Title:
|
The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem (English) |
| Author:
|
Cichoń, M. |
| Author:
|
Kubiaczyk, I. |
| Author:
|
Sikorska, A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
279-289 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove an existence theorem for the Cauchy problem \[ x^{\prime }(t) = f(t, x(t)), \quad x(0) = x_0, \quad t \in I_{\alpha } = [0, \alpha ] \] using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function $f$ are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function $f$ satisfies some conditions expressed in terms of measures of weak noncompactness. (English) |
| Keyword:
|
pseudo-solution |
| Keyword:
|
Pettis integral |
| Keyword:
|
Henstock-Kurzweil integral |
| Keyword:
|
Cauchy problem |
| MSC:
|
28B05 |
| MSC:
|
34G20 |
| idZBL:
|
Zbl 1080.34550 |
| idMR:
|
MR2059250 |
| . |
| Date available:
|
2009-09-24T11:12:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127887 |
| . |
| Reference:
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