| Title:
|
Boundary value problems for higher order ordinary differential equations (English) |
| Author:
|
Majorana, Armando |
| Author:
|
Marano, Salvatore A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
451-466 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $f : [a,b] \times \Bbb R^{n+1} \rightarrow \Bbb R$ be a Carath'{e}odory's function. Let $ \{t_{h}\} $, with $t_{h} \in [a,b]$, and $\{x_{h}\}$ be two real sequences. In this paper, the family of boundary value problems $$ \cases x^{(k)} = f \left( t,x,x',\ldots ,x^{(n)} \right) \ x^{(i)}(t_{i}) = x_{i} \,, \quad i=0,1, \ldots , k-1 \endcases \qquad (k=n+1,n+2,n+3,\ldots ) $$ is considered. It is proved that these boundary value problems admit at least a solution for each $k \geq \nu$, where $\nu \geq n+1$ is a suitable integer. Some particular cases, obtained by specializing the sequence $\{t_{h}\}$, are pointed out. Similar results are also proved for the Picard problem. (English) |
| Keyword:
|
higher order ordinary differential equations |
| Keyword:
|
Nicoletti problem |
| Keyword:
|
Picard \newline problem |
| MSC:
|
34A12 |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 0809.34034 |
| idMR:
|
MR1307273 |
| . |
| Date available:
|
2009-01-08T18:12:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118686 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| . |
