Geodesic
Solvability of nonlinear equations in a cone of a Banach space
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 225-230

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

The solvability conditions for the equation $Tu+F(u)=0$ are found in the case where the operator $[T+F'(u)]^{-1}$ exists only for $u\in K$, where $K$ is a cone in the Banach space $X$. An application concerning the solvability of boundary-value problems for a system of second-order differential equations is provided. 
@article{ZNSL_1998_248_a11,
     author = {M. N. Yakovlev},
     title = {Solvability of nonlinear equations in a cone of a {Banach} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {225--230},
     publisher = {mathdoc},
     volume = {248},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a11/}
}
TY  - JOUR
AU  - M. N. Yakovlev
TI  - Solvability of nonlinear equations in a cone of a Banach space
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1998
SP  - 225
EP  - 230
VL  - 248
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a11/
LA  - ru
ID  - ZNSL_1998_248_a11
ER  - 
%0 Journal Article
%A M. N. Yakovlev
%T Solvability of nonlinear equations in a cone of a Banach space
%J Zapiski Nauchnykh Seminarov POMI
%D 1998
%P 225-230
%V 248
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a11/
%G ru
%F ZNSL_1998_248_a11
M. N. Yakovlev. Solvability of nonlinear equations in a cone of a Banach space. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 225-230. http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a11/