Thesis-2006-Barnett.pdf (1.61 MB)
Applications of Nevanlinna theory to q-difference equations
thesisposted on 2018-08-15, 08:18 authored by David C. Barnett
Recently 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.
Engineering and Physical Sciences Research Council.
- Mathematical Sciences
Publisher© David Barnett
Publisher statementThis 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/
NotesA Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.