| Title:
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On Kneser solutions of the $n$-th order nonlinear differential inclusions (English) |
| Author:
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Pavlačková, Martina |
| Language:
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English |
| Journal:
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Czechoslovak Mathematical Journal |
| ISSN:
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0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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69 |
| Issue:
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1 |
| Year:
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2019 |
| Pages:
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99-116 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
|
The paper deals with the existence of a Kneser solution of the $n$-th order nonlinear differential inclusion \begin {eqnarray} {x}^{(n)}(t)\in -A_{1}(t,x(t),\ldots ,x^{(n-1)}(t)){x}^{(n-1)}(t)-\ldots -A_{n}(t,x(t),\ldots ,&x^{(n-1)}(t))x(t)\nonumber \\ &\text {for a.a.} \ t\in [a,\infty ),\nonumber \end {eqnarray} where $a\in (0,\infty )$, and $A_i\colon [a,\infty ) \times \mathbb {R}^{n}\to \mathbb {R}$, $i=1,\ldots ,n,$ are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem. (English) |
| Keyword:
|
asymptotic $n$-th order vector problems |
| Keyword:
|
$R_{\delta }$-set |
| Keyword:
|
inverse limit technique |
| Keyword:
|
Kneser problem |
| MSC:
|
34A60 |
| MSC:
|
34B15 |
| MSC:
|
34B40 |
| idZBL:
|
Zbl 07088773 |
| idMR:
|
MR3923578 |
| DOI:
|
10.21136/CMJ.2018.0191-17 |
| . |
| Date available:
|
2019-03-08T14:57:35Z |
| Last updated:
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2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147621 |
| . |
| Reference:
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