\(C^m\) solutions of systems of finite difference equations. (English) Zbl 1036.39003

Liu, Xinhe; Zhao, Xiuli; Ma, Jianmin

Int. J. Math. Math. Sci. 2003, No. 36, 2315-2326 (2003).

Under certain conditions it is shown for given \(G\), \(H\) that the system \[ G(x, f(x),\dots, f(x+ n), g(x),\dots, g(x+ n))= 0, \]
\[ H(x,g(x),\dots, g(x+ n), f(x),\dots, f(x+ n))= 0 \] has a unique solution \(f\), \(g\) in \(\mathbb{C}^m\).

Reviewer: Lothar Berg (Rostock)

MSC:

39A10	Additive difference equations
39A20	Multiplicative and other generalized difference equations

Keywords:

system of difference equations