Thesis-2006-Barnett.pdf (1.61 MB)
Applications of Nevanlinna theory to q-difference equations
thesis
posted on 2018-08-15, 08:18 authored by David C. BarnettRecently Nevanlinna theory (the theory of meromorphic functions) has been used as
a detector of integrability of difference equations. In this thesis we study meromorphic
solutions of so-called q-difference equations and extend some key results from
Nevanlinna theory to the q-difference operator.
The Lemma on the Logarithmic Derivative of a meromorphic function has many
applications in the study of meromorphic functions and ordinary differential equations.
In this thesis, a q-difference analogue of the Logarithmic Derivative Lemma is
presented, and then applied to prove a number of results on meromorphic solutions
of complex q-difference equations. These results include a difference analogue of the
Clunie Lemma, as well as other results on the value distribution of solutions.
Funding
Engineering and Physical Sciences Research Council.
History
School
- Science
Department
- Mathematical Sciences
Publisher
© David BarnettPublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2006Notes
A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.Language
- en