Periodic behaviour of nonlinear, second-order discrete dynamical systems. Issue 2 (1st February 2016) - Maroncelli, Daniel; Rodríguez, Jesús
Abstract : In this work, we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form y ( t + 2 ) + b y ( t + 1 ) + c y ( 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.