| Title:
|
On the opial type criterion for the well-posedness of the Cauchy problem for linear systems of generalized ordinary differential equations (English) |
| Author:
|
Ashordia, Malkhaz |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
183-215 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense ${\rm d} x(t)={\rm d} A_0(t)\cdot x(t)+{\rm d} f_0(t)$, $x(t_{0})=\nobreak c_0$ $(t\in I)$ with a unique solution $x_0$ is considered. Necessary and sufficient conditions are obtained for a sequence of the Cauchy problems ${\rm d} x(t)={\rm d} A_k(t)\cdot x(t)+{\rm d} f_k(t)$, $x(t_{k})=c_k$ $(k=1,2,\dots )$ to have a unique solution $x_k$ for any sufficiently large $k$ such that $x_k(t)\to x_0(t)$ uniformly on $I$. Presented results are analogous to the sufficient conditions due to Z. Opial for linear ordinary differential systems. Moreover, efficient sufficient conditions for the problem of well-posedness are given. (English) |
| Keyword:
|
linear system of generalized ordinary differential equations in the Kurzweil sense |
| Keyword:
|
Cauchy problem |
| Keyword:
|
well-posedness |
| Keyword:
|
Opial type necessary condition |
| Keyword:
|
Opial type sufficient condition |
| Keyword:
|
efficient sufficient condition |
| MSC:
|
34A12 |
| MSC:
|
34A30 |
| MSC:
|
34K06 |
| idZBL:
|
Zbl 06587862 |
| idMR:
|
MR3499784 |
| DOI:
|
10.21136/MB.2016.15 |
| . |
| Date available:
|
2016-05-19T09:06:31Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145712 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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