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On the solvability of initial-value problems for nonlinear implicit difference equations
Advances in Difference Equations volume 2004, Article number: 390451 (2004)
Our aim is twofold. First, we propose a natural definition of index for linear nonautonomous implicit difference equations, which is similar to that of linear differential-algebraic equations. Then we extend this index notion to a class of nonlinear implicit difference equations and prove some existence theorems for their initial-value problems.
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Anh, P.K., Yen, H.T.N. On the solvability of initial-value problems for nonlinear implicit difference equations. Adv Differ Equ 2004, 390451 (2004). https://doi.org/10.1155/S1687183904402015