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Periodic and asymptotically periodic solutions of the nonlinear equation Δx + af(x) = 0, n ∈ N, are studied.
In the paper sufficient conditions for the difference equation :
Δxn = Σi=0
r an
(i) xn+i
to have a solution which tends to a constant, are given. Applying these conditions, an asymptotic formula for a solution of an m-th order equation is presented.
For the linear difference equation
sufficient conditions for the existence of an asymptotically periodic solutions are given.
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