Asymptotic behavior of the solutions of the second order difference equation

Drozdowicz, Andrzej; Popenda, Jerzy

doi:10.1090/S0002-9939-1987-0866443-0

Asymptotic behavior of the solutions of the second order difference equation
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by Andrzej Drozdowicz and Jerzy Popenda PDF

Proc. Amer. Math. Soc. 99 (1987), 135-140 Request permission

Abstract:

The second order difference equation (E) \[ {\Delta ^2}{x_n} + {p_n}f({x_n}) = 0\] is considered. The results give a necessary and sufficient condition for some solution of (E) to have asymptotic behavior ${x_n} \sim C = \text {const}$. as $n$ approaches infinity.

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