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 paper, a difference analogueâ€¦ (More)

Certain estimates involving the derivative f 7â†’ f â€² of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose of this study is toâ€¦ (More)

R.G. Halburdâˆ— Department of Mathematical Sciences, Loughborough University Loughborough, Leicestershire, LE11 3TU, UK (Dated: January 21, 2005) Abstract The heights of iterates of the discreteâ€¦ (More)

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there isâ€¦ (More)

A third-order system of nonlinear, ordinary differential equations depending on 3 arbitrary parameters is analyzed. The system arises in the study of SU(2)-invariant hypercomplex manifolds and is aâ€¦ (More)

It is shown that, if f is a meromorphic function of order zero and q âˆˆ C, then m â€ž r, f(qz) f(z) Â« = o(T (r, f)) (â€¡) for all r on a set of logarithmic density 1. The remainder of the paper consist ofâ€¦ (More)

A tropical version of Nevanlinna theory is described in which the role of meromorphic functions is played by continuous piecewise linear functions of a real variable whose one-sided derivatives areâ€¦ (More)

Any nonlinear equation of the form yâ€²â€² = âˆ‘N n=0 an(z)y n has a (generally branched) solution with leading order behaviour proportional to (z âˆ’ z0) about a point z0, where the coefficients an areâ€¦ (More)