| Title:
|
On boundary value problems for systems of nonlinear generalized ordinary differential equations (English) |
| Author:
|
Ashordia, Malkhaz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
579-608 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A general theorem (principle of a priori boundedness) on solvability of the boundary value problem $$ {\rm d} x={\rm d} A(t)\cdot f(t,x),\quad h(x)=0 $$ is established, where $f\colon [a,b]\times \mathbb {R}^n\to \mathbb {R}^n$ is a vector-function belonging to the Carathéodory class corresponding to the matrix-function $A\colon [a,b]\to \mathbb {R}^{n\times n}$ with bounded total variation components, and $h\colon \operatorname {BV}_s([a,b],\mathbb {R}^n)\to \mathbb {R}^n$ is a continuous operator. Basing on the mentioned principle of a priori boundedness, effective criteria are obtained for the solvability of the system under the condition $x(t_1(x))=\mathcal {B}(x)\cdot x(t_2(x))+c_0,$ where $t_i\colon \operatorname {BV}_s([a,b],\mathbb {R}^{n})\to [a,b]$ $(i=1,2)$ and $\mathcal {B}\colon \operatorname {BV}_s([a,b],\mathbb {R}^{n})\to \mathbb {R}^n$ are continuous operators, and $c_0\in \mathbb {R}^n$. (English) |
| Keyword:
|
system of nonlinear generalized ordinary differential equations |
| Keyword:
|
Kurzweil-Stieltjes integral |
| Keyword:
|
general boundary value problem |
| Keyword:
|
solvability |
| Keyword:
|
principle of a priori boundedness |
| MSC:
|
34K10 |
| idZBL:
|
Zbl 06770119 |
| idMR:
|
MR3697905 |
| DOI:
|
10.21136/CMJ.2017.0144-11 |
| . |
| Date available:
|
2017-09-01T12:19:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146847 |
| . |
| Reference:
|
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| Reference:
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