Geodesic
The method of local linear approximation in the theory of nonlinear functional-differential equations
Sbornik. Mathematics, Tome 201 (2010) no. 8, pp. 1193-1215

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

Conditions for the existence of solutions to the nonlinear functional-differential equation $$ \frac{d^mx(t)}{dt^m}+(Fx)(t)=h(t), \qquad t\in\mathbb R, $$ in the space of functions bounded on the axes are obtained by using local linear approximation to the operator $F$. Bibliography: 21 items.
Keywords: functional-differential equations, invertibility of nonlinear operators. 
@article{SM_2010_201_8_a5,
     author = {V. E. Slyusarchuk},
     title = {The method of local linear approximation in the theory of nonlinear functional-differential equations},
     journal = {Sbornik. Mathematics},
     pages = {1193--1215},
     publisher = {mathdoc},
     volume = {201},
     number = {8},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_8_a5/}
}
TY  - JOUR
AU  - V. E. Slyusarchuk
TI  - The method of local linear approximation in the theory of nonlinear functional-differential equations
JO  - Sbornik. Mathematics
PY  - 2010
SP  - 1193
EP  - 1215
VL  - 201
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2010_201_8_a5/
LA  - en
ID  - SM_2010_201_8_a5
ER  - 
%0 Journal Article
%A V. E. Slyusarchuk
%T The method of local linear approximation in the theory of nonlinear functional-differential equations
%J Sbornik. Mathematics
%D 2010
%P 1193-1215
%V 201
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2010_201_8_a5/
%G en
%F SM_2010_201_8_a5
V. E. Slyusarchuk. The method of local linear approximation in the theory of nonlinear functional-differential equations. Sbornik. Mathematics, Tome 201 (2010) no. 8, pp. 1193-1215. http://geodesic.mathdoc.fr/item/SM_2010_201_8_a5/