The Existence of Solutions for a Nonlinear, Fractional Self-Adjoint Difference Equation

Authors

Kevin Ahrendt, University of Nebraska-LincolnFollow

First Advisor

Allan C. Peterson

Date of this Version

4-2017

Document Type

Article

Citation

Kevin Ahrendt. The Existence of Solutions for a Nonlinear, Fractional Self-Adjoint Difference Equation. PhD thesis, University of Nebraska-Lincoln, 2017.

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Allan Peterson. Lincoln, Nebraska: April, 2017

Copyright (c) 2017 Kevin Ahrendt

Abstract

In this work we will explore a fractional self-adjoint difference equation which involves a Caputo fractional difference. In particular, we will develop a Cauchy function for initial value problems and Green's functions for several different types of boundary value problems. We will use the properties of those Green's functions and the Contraction Mapping Theorem to find sufficient conditions for when a nonlinear boundary value problem has a unique solution. We will also investigate the existence of nonnegative solutions for a nonlinear self-adjoint difference that have particular long run behavior.

Adviser: Allan Peterson