Periodic behaviour of nonlinear, second-order discrete dynamical systems

In this work, we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the formy(t+2)+by(t+1)+cy(t)=g(t,y(t))where c≠0, and g:Z+×R→R is continuous and periodic in t. Our analysis uses the Lyapunov–Schmidt reduction in combination with fixed point methods and topological degree theory.