Geodesic
On estimates for the Green's function for a multipoint boundary problem
Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 533-540 
Yu. V. Pokornyi. On estimates for the Green's function for a multipoint boundary problem. Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 533-540. http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a5/
@article{MZM_1968_4_5_a5,
     author = {Yu. V. Pokornyi},
     title = {On estimates for the {Green's} function for a~multipoint boundary problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {533--540},
     year = {1968},
     volume = {4},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a5/}
}
TY  - JOUR
AU  - Yu. V. Pokornyi
TI  - On estimates for the Green's function for a multipoint boundary problem
JO  - Matematičeskie zametki
PY  - 1968
SP  - 533
EP  - 540
VL  - 4
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a5/
LA  - ru
ID  - MZM_1968_4_5_a5
ER  - 
%0 Journal Article
%A Yu. V. Pokornyi
%T On estimates for the Green's function for a multipoint boundary problem
%J Matematičeskie zametki
%D 1968
%P 533-540
%V 4
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a5/
%G ru
%F MZM_1968_4_5_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain new estimates for the Green's function $G(t,\,s)$ for a boundary problem of the Vallée-Poussin type: under certain hypotheses we prove the existence of non-negative functions $g(t)$, $h(t)$, $u(t)$ such that $g(t)h(s)\le|G(t,s)|\le g(t)$ and $|G(t,s)|\ge u(t)\max\limits_\tau|G(\tau,s)|$, where $h(t)$ and $u(t)$ are positive on sets of positive measure. These estimates allow us to apply effectively the methods of the theory of cones to investigate non-linear boundary problems.