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Advances in Continuous and Discrete Models

Theory and Modern Applications

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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) Cite this article

Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Mechanics, and Informatics, College of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Pham Ky Anh

  2. Department of Applied Mathematics, Hanoi University of Technology, 1 Dai Co Viet, Hanoi, 10000, Vietnam

    Ha Thi Ngoc Yen

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  1. Pham Ky Anh
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  2. Ha Thi Ngoc Yen
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Correspondence to Pham Ky Anh.

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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

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  • DOI: https://doi.org/10.1155/S1687183904402015