Advances in Difference Equations
Volume 2004 (2004), Issue 3, Pages 195-200

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

Pham Ky Anh1 and Ha Thi Ngoc Yen2

1Department of Mathematics, Mechanics, and Informatics, College of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
2Department of Applied Mathematics, Hanoi University of Technology, 1 Dai Co Viet, Hanoi 10000, Vietnam

Received 18 February 2004

Copyright © 2004 Pham Ky Anh and Ha Thi Ngoc Yen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.