Approximative Full Solutions of Difference Equations

In the study of asymptotic properties of solutions of difference equations, so called generalized solutions are often considered, that is, sequences for which a given equation is satisfied from some starting point. In this paper we establish conditions which allow us to control the starting point. Moreover, we establish conditions which allow us to change some finite terms of generalized solutions so that a full solution is obtained. AMS Subject Classifications: 39A10.