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arXiv · 1511.03909

Periodic behaviour of nonlinear second order discrete dynamical systems

Daniel Maroncelli·Jesus Rodriguez
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Abstract

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.

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BibTeXRIS

Daniel Maroncelli, Jesus Rodriguez. 2015-11-12. Periodic behaviour of nonlinear second order discrete dynamical systems. https://doi.org/10.1080/10236198.2015.1083016

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