Boundary value problems for higher order ordinary differential equations

Majorana, Armando, and Marano, Salvatore A.. "Boundary value problems for higher order ordinary differential equations." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 451-466. <http://eudml.org/doc/247613>.

@article{Majorana1994,
abstract = {Let $f : [a,b] \times \mathbb \{R\}^\{n+1\} \rightarrow \mathbb \{R\}$ be a Carath’eodory’s function. Let $ \lbrace t_\{h\}\rbrace $, with $t_\{h\} \in [a,b]$, and $\lbrace x_\{h\}\rbrace $ be two real sequences. In this paper, the family of boundary value problems \[ \left\lbrace \begin\{array\}\{ll\}x^\{(k)\} = f \left( t,x,x^\{\prime \},\ldots ,x^\{(n)\} \right) \ x^\{(i)\}(t\_\{i\}) = x\_\{i\} \,, \quad i=0,1, \ldots , k-1 \end\{array\}\right.\qquad (k=n+1,n+2,n+3,\ldots ) \] is considered. It is proved that these boundary value problems admit at least a solution for each $k \ge \nu $, where $\nu \ge n+1$ is a suitable integer. Some particular cases, obtained by specializing the sequence $\lbrace t_\{h\}\rbrace $, are pointed out. Similar results are also proved for the Picard problem.},
author = {Majorana, Armando, Marano, Salvatore A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {higher order ordinary differential equations; Nicoletti problem; Picard problem; Schauder fixed point theorem; Abel-Gontcharoff and Lagrange polynomials; existence},
language = {eng},
number = {3},
pages = {451-466},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Boundary value problems for higher order ordinary differential equations},
url = {http://eudml.org/doc/247613},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Majorana, Armando
AU - Marano, Salvatore A.
TI - Boundary value problems for higher order ordinary differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 451
EP - 466
AB - Let $f : [a,b] \times \mathbb {R}^{n+1} \rightarrow \mathbb {R}$ be a Carath’eodory’s function. Let $ \lbrace t_{h}\rbrace $, with $t_{h} \in [a,b]$, and $\lbrace x_{h}\rbrace $ be two real sequences. In this paper, the family of boundary value problems \[ \left\lbrace \begin{array}{ll}x^{(k)} = f \left( t,x,x^{\prime },\ldots ,x^{(n)} \right) \ x^{(i)}(t_{i}) = x_{i} \,, \quad i=0,1, \ldots , k-1 \end{array}\right.\qquad (k=n+1,n+2,n+3,\ldots ) \] is considered. It is proved that these boundary value problems admit at least a solution for each $k \ge \nu $, where $\nu \ge n+1$ is a suitable integer. Some particular cases, obtained by specializing the sequence $\lbrace t_{h}\rbrace $, are pointed out. Similar results are also proved for the Picard problem.
LA - eng
KW - higher order ordinary differential equations; Nicoletti problem; Picard problem; Schauder fixed point theorem; Abel-Gontcharoff and Lagrange polynomials; existence
UR - http://eudml.org/doc/247613
ER -