The purpose of this paper is to discuss the relationship between the characteristic function of an E-valued meromorphic function f and and that of its derivative f ′. Consequently, for a finite order E-valued meromorphic function f with maximal deficiency sum, we obtain that T (r, f ′) ∼ (2 − δ(∞̂, f))T (r, f) as r → +∞. Results are obtained to extend the related results for meromorphic scalar v...

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 analogue of the Logarithmic Derivative Lemma is presented, and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue...

We consider the n × n matrix linear differential systems in the complex plane. We find necessary and sufficient conditions under which these systems have meromorphic fundamental solutions. Using the operator identity method we construct a set of systems which have meromorphic solutions. We prove that the well known operator with the sine kernel generates a class of meromorphic Painlevé type fun...

Let a0, . . . , ak−1 be analytic functions on a domain Ω. Let F be a family of meromorphic functions f on Ω such that f 6= 0 and f (k) + ak−1f (k−1) + . . . + a0f 6= 0 on Ω, for all f ∈ F . Then {f ′/f : f ∈ F} is a normal family. Furthermore, let a0, . . . , ak−1 be meromorphic functions on a domain Ω. Let F be a family of meromorphic functions f on Ω such that f 6= 0, f ′ 6= 0 and f (k) + ak−...