Geodesic
On estimates for the Green's function for a~multipoint boundary problem
Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 533-540

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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. 
@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},
     publisher = {mathdoc},
     volume = {4},
     number = {5},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a5/}
}
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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/