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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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