Geodesic
Conditions for the invertibility of the nonlinear difference operator
Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 261-282

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Necessary and sufficient conditions are found for the invertibility of the nonlinear difference operator $$ (\mathscr Rx)(n)=H(x(n),x(n+1)),\qquad n\in\mathbb Z, $$ in the space of bounded two-sided number sequences. Here $H\colon \mathbb R^2\to \mathbb R $ is a continuous function. Bibliography: 29 titles.
Keywords: invertibility of a nonlinear operator, telegraph equations. 
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     author = {V. E. Slyusarchuk},
     title = {Conditions for the invertibility of the nonlinear difference operator},
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V. E. Slyusarchuk. Conditions for the invertibility of the nonlinear difference operator. Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 261-282. http://geodesic.mathdoc.fr/item/SM_2009_200_2_a5/