Periodic behaviour of nonlinear second order discrete dynamical systems

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