Prefer a chat interface with context about you and your work?
Asymptotic Behavior of the Solutions of the Second Order Difference Equation
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.