Second Order Rational Difference Equation Research Articles

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second-order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

When does periodicity destroy boundedness in rational equations?

Our goal here is to present some results and to pose several open problems and conjectures related to the question in the title as applied to the second-order rational difference equation with nonn...

Boundedness of Positive Solutions of Second-order Rational Difference Equations

We study positive solutions for all second-order rational difference equations with nonnegative coefficients of the form: We obtain necessary and sufficient conditions that their positive solutions are bounded. These results provide solutions to several open problems and conjectures proposed by M.R.S. Kulenović and G. Ladas.