On the global attractivity and oscillations in a class of second order difference equations from macroeconomics

New global attractivity criteria are obtained for the second order difference equation $$x_{n+1}=c{x}_n+f(x_n-x_{n-1}),n=1,2,\mathrm{.}\mathrm{.}\mathrm{.}$$ via a Lyapunov-like method. Some of these results are sharp and support recent related conjectures. Also, a necessary and sufficient condition for the oscillation of this equation is obtained using comparison with a second order linear difference equation with positive coefficients.