Asymptotically periodic solutions of second order difference equations

Abstract In this paper, we obtain sufficient conditions for the existence of asymptotically periodic solutions of the second order difference equations of the form Δ ( r n Δ x n ) = a n f ( x n − τ ) + b n . Moreover, we give sufficient conditions under which every bounded solution of the above equation is asymptotically periodic. Our approach allows us to control the degree of approximation.

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