Uniqueness of solutions of simultaneous difference equations

Abstract. We study the uniqueness of continuous, continuous at a point as well as monotonic solutions of some simultaneous linear difference equations, in the case when individual equations usually have a lot of solutions in the considered class of functions. Also the general solution on cosets of the group generated by the set of numbers parametrizing the equations has been given.

Key words and phrases. Simultaneous difference equations, continuous solution, monotonic solution, uniqueness of solutions, Cauchy functional equation, group generated.