Reduction of Order, Periodicity and Boundedness in Nonlinear, Higher Order Difference Equations
arXiv:1203.5743 · doi:10.1016/j.camwa.2013.06.019
Abstract
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and economics. By extending some recent results to cases where characteristic polynomials of the linear expressions have complex roots, we obtain new results on boundedness and the existence of periodic solutions for equations of order 3 or greater.
arXiv comment14 pages