Thesis-2006-Barnett.pdf (1.61 MB)
Download fileApplications of Nevanlinna theory to q-difference equations
thesis
posted on 15.08.2018, 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