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On the solvability of initial-value problems for nonlinear implicit difference equations

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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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Correspondence to Pham Ky Anh.

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