Global behavior of a rational second order difference equation
The authors study a particular nonlinear rational difference-functional equation. By means of a transformation, the equation is transformed into a linear third-order difference-functional equation. To find its solutions, three cases are considered. These cases are not considered in the book [\textit{M. Kuczma}, An introduction to the theory of functional equations and inequalities. Cauchy's equation and Jensen's inequality. Edited by Attila Gilányi. Basel: Birkhäuser (2009; Zbl 1221.39041)]. The authors consider the global behavior of the original nonlinear rational difference-functional equation by using standard methods known in the literature. Under some additional assumptions they also construct periodic and converging to periodic solutions.
scientific article; zbMATH DE number 7435251
scientific article