Geodesic
On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1033-1053.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Consider the homogeneous equation $$ u'(t)=\ell (u)(t)\qquad \mbox {for a.e. } t\in [a,b] $$ where $\ell \colon C([a,b];\Bbb R)\to L([a,b];\Bbb R)$ is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.
DOI : 10.1007/s10587-012-0062-1
Classification : 34K06, 34K10
Keywords: functional differential equation; boundary value problem; differential inequality; solution set 
@article{10_1007_s10587_012_0062_1,
     author = {Domoshnitsky, Alexander and Hakl, Robert and P\r{u}\v{z}a, Bed\v{r}ich},
     title = {On the dimension of the solution set to the homogeneous linear functional differential equation of the first order},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1033--1053},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2012},
     doi = {10.1007/s10587-012-0062-1},
     mrnumber = {3010255},
     zbl = {1274.34184},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0062-1/}
}
TY  - JOUR
AU  - Domoshnitsky, Alexander
AU  - Hakl, Robert
AU  - Půža, Bedřich
TI  - On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 1033
EP  - 1053
VL  - 62
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0062-1/
DO  - 10.1007/s10587-012-0062-1
LA  - en
ID  - 10_1007_s10587_012_0062_1
ER  - 
%0 Journal Article
%A Domoshnitsky, Alexander
%A Hakl, Robert
%A Půža, Bedřich
%T On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
%J Czechoslovak Mathematical Journal
%D 2012
%P 1033-1053
%V 62
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0062-1/
%R 10.1007/s10587-012-0062-1
%G en
%F 10_1007_s10587_012_0062_1
Domoshnitsky, Alexander; Hakl, Robert; Půža, Bedřich. On the dimension of the solution set to the homogeneous linear functional differential equation of the first order. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1033-1053. doi : 10.1007/s10587-012-0062-1. http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0062-1/

Cité par Sources :