This paper deals with an index-2 notion for linear implicit difference equations (LIDEs) and with the solvability of initial value problems (IVPs) for index-2 LIDEs. Besides, the cocycle property as well as the multiplicative ergodic theorem of Oseledets type are also proved. © 2010 Elsevier Inc. All rights reserved.

Du N.H., Loi L.C., Duy T.K., Viet V.T.

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Từ khóa : Differential algebraic equations; Index; Initial values; Linear implicit; Lyapunov exponent; Random dynamics; Algebra; Difference equations; Initial value problems; Lyapunov functions; Lyapunov methods; Theorem proving; Least squares approximations