The Cauchy problem for partial difference equations (Q1273481)

The author obtains general results about the existence and uniqueness of solutions for linear equations with variable coefficients considered on arbitrary subsets of \(\mathbb{Z}^n\) and also for large classes of nonlinear partial difference equations. The construction of solutions presented here also allows for some qualitative conclusions, such as boundedness of solutions. For related results see the papers of \textit{U. Oberst} [Acta Appl. Math. 20, No. 1/2, 1-175 (1990; Zbl 0715.93014)] and \textit{S. Zampieri} [Linear Algebra Appl. 202, 143-162 (1994; Zbl 0802.93036)].