Advances in Difference Equations
Volume 2004 (2004), Issue 3, Pages 195-200
doi:10.1155/S1687183904402015
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
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.