Geodesic
Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k + j)-Point Boundary Value Problems for n-th Order Differential Equations
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 285-296

Voir la notice de l'article provenant de la source Cambridge

DOI

For the $n$ -th order nonlinear differential equation, ${{y}^{(n)}}\,=\,f(x,\,y,\,y\prime ,\ldots ,\,{{y}^{(n-1)}})$ , we consider uniqueness implies uniqueness and existence results for solutions satisfying certain $(k\,+\,j)$ -point boundary conditions for $1\,\le \,j\,\le \,n\,-\,1$ and $1\,\le \,k\,\le \,n\,-\,j$ . We define $(k;\,j)$ -point unique solvability in analogy to $k$ -point disconjugacy and we show that $(n\,-\,{{j}_{0}};\,{{j}_{0}})$ -point unique solvability implies $(k;\,j)$ -point unique solvability for $1\,\le \,j\,\le \,{{j}_{0}}$ , and $1\,\le \,k\,\le \,n\,-\,j$ . This result is analogous to $n$ -point disconjugacy implies $k$ -point disconjugacy for $2\,\le \,k\,\le \,n\,-\,1$ .
DOI : 10.4153/CMB-2011-117-0
Mots-clés : 34B15, 34B10, 65D05, boundary value problem, uniqueness, existence, unique solvability, nonlinear interpolation 
Eloe, Paul W.; Henderson, Johnny; Khan, Rahmat Ali. Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k + j)-Point Boundary Value Problems for n-th Order Differential Equations. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 285-296. doi: 10.4153/CMB-2011-117-0
@article{10_4153_CMB_2011_117_0,
     author = {Eloe, Paul W. and Henderson, Johnny and Khan, Rahmat Ali},
     title = {Uniqueness {Implies} {Existence} and {Uniqueness} {Conditions} for a {Class} of (k + {j)-Point} {Boundary} {Value} {Problems} for n-th {Order} {Differential} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {285--296},
     year = {2012},
     volume = {55},
     number = {2},
     doi = {10.4153/CMB-2011-117-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-117-0/}
}
TY  - JOUR
AU  - Eloe, Paul W.
AU  - Henderson, Johnny
AU  - Khan, Rahmat Ali
TI  - Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k + j)-Point Boundary Value Problems for n-th Order Differential Equations
JO  - Canadian mathematical bulletin
PY  - 2012
SP  - 285
EP  - 296
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-117-0/
DO  - 10.4153/CMB-2011-117-0
ID  - 10_4153_CMB_2011_117_0
ER  - 
%0 Journal Article
%A Eloe, Paul W.
%A Henderson, Johnny
%A Khan, Rahmat Ali
%T Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k + j)-Point Boundary Value Problems for n-th Order Differential Equations
%J Canadian mathematical bulletin
%D 2012
%P 285-296
%V 55
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-117-0/
%R 10.4153/CMB-2011-117-0
%F 10_4153_CMB_2011_117_0

Cité par Sources :