Qualitative approximation of solutions to difference equations of various types

In this paper we study the asymptotic behavior of solutions to difference equations of various types. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, and establish some results concerning approximations of solutions, extending some of our previous results. Our approach allows us to control the degree of approximation. As a measure of approximation we use o(u(n)) where u is an arbitrary fixed positive nonincreasing sequence.