# Difference equation with non-linear term

by Busi
Tags: difference, equation, nonlinear, term
 P: 1 Hi all-- I can't figure out how to approach the following difference equation: ax_{t}+f(x_{t-1})+bx_{t-2}=e_{t} where a, b are constants, e_t is a known function and f(x_t-1) is a convex, u-shaped function that goes through the origin. (Sorry Tex would not want to work) To begin with, I considered f linear and solved the equation. Exactly one of the roots of the corresponding homogenous equation lies within the unit circle, so I set the free coefficients in the general solution to zero to obtain a bounded solution and derive the particular solution. Does anyone know a way to treat a nonlinear function f?

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