Periodicity, convergence, and boundedness of some difference equations

Author

Carol Herchen Gibbons, University of Rhode Island

Date of Award

2003

Degree Type

Dissertation

First Advisor

Gerasimos Ladas

Abstract

We investigate the periodicity, the boundedness, and the convergence of the solutions of several difference equations. The first equation is [special characters omitted] For this equation, we give a detailed description of the trichotomy behavior of solutions, which depends on the relative values of the parameters β and γ. The second equation is [special characters omitted] For this equation, the trichotomy nature of the solutions is shown to hold, where the trichotomy depends upon the values of γ, β, and A. We also investigate the nature of the solutions of the general equation [special characters omitted] For this equation, we present many open problems and conjectures related to the existence of solutions for which a trichotomy character holds. For all equations, the parameters and initial conditions are taken to be nonnegative real numbers.

Recommended Citation

Gibbons, Carol Herchen, "Periodicity, convergence, and boundedness of some difference equations" (2003). Open Access Dissertations. Paper 1873.
https://digitalcommons.uri.edu/oa_diss/1873