  In this work we provide conditions for the existence of periodic solutions to
nonlinear, second-order difference equations of the form \begin{equation*}
y(t+2)+by(t+1)+cy(t)=g(t,y(t)) \end{equation*} where $c\neq 0$, and
$g:\mathbb{Z}^+\times\mathbb{R}\to \mathbb{R}$ is continuous and periodic in
$t$. Our analysis uses the Lyapunov-Schmidt reduction in combination with fixed
point methods and topological degree theory.
