ABSTRACT
Put ∆u(k) := u(k + 1) − u(k). Let us consider a scalar discrete equation containing one difference
∆u(k) = f(k, u(k)) (2)
with a one-valued function f : N(a) × R → R and a ∈ N. Together with discrete Equation (2) we consider an initial problem. It is posed as follows: for a given s ∈ N∗ we are seeking the solution u = u(k) of (2) satisfying the initial condition
u(a+ s) = us ∈ R (3) with a prescribed constant us. Let us recall that the solution of initial problem (2), (3) is defined as an infinite sequence of numbers
{ uk }∞
0 with uk = u(a+
s+ k), i.e.
