Periodic behaviour of nonlinear, second-order discrete dynamical systems. Issue 2 (1st February 2016)

• Record Type: Journal Article
• Authors: Maroncelli, Daniel; Rodríguez, Jesús
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 2(2016)
• Page Start: 280
• Page End: 294
• Publication Date: 2016-02-01
• Subjects: Periodic difference equations -- resonance -- Lyapunov–Schmidt procedure -- Schauder's fixed point theorem -- topological degree; 34B15; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2015.1083016
• Languages: English
• ISSNs: 1023-6198

Abstract

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.