Boundary value problems for higher order ordinary differential equations
Majorana, Armando ; Marano, Salvatore A.
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 451-466 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1994-01-01
Classification:  34A12,  34B10,  34B15 
@article{118686,
     author = {Armando Majorana and Salvatore A. Marano},
     title = {Boundary value problems for higher order ordinary differential equations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {451-466},
     zbl = {0809.34034},
     mrnumber = {1307273},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118686}
}

Majorana, Armando; Marano, Salvatore A. Boundary value problems for higher order ordinary differential equations. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 451-466. http://gdmltest.u-ga.fr/item/118686/

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