THE CAUCHY-PROBLEM FOR PARTIAL DIFFERENCE-EQUATIONS

We want to discuss partial difference equations, first of all with res pect to the existence and uniqueness of their solution. These equation s are considered with solutions on arbitrary subsets of the n-dimensio nal grid Z(n). The basic theorem enables one to formulate the Cauchy p roblem for such equations. The solution is proven to be recursively co mputable for partial difference equations under very mild restrictions . (Variable coefficients for Linear equations, systems of equations as well as nonlinear equations are not excluded.) The construction of so lutions presented here also allows for some qualitative conclusions, s uch as boundedness of solutions.