Hi all--(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Difference equation with non-linear term

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**