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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:
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