Related papers: Logarithmic difference lemma in several complex va…
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…
The maximum of the modulus of a meromorphic function cannot be restricted from above by the Nevanlinna characteristic of this meromorphic function. But integrals from the logarithm of the module of a meromorphic function allow similar…
The first objective of the paper is to estimate logarithmic partial derivative for meromorphic functions in several complex variables. Our estimations for logarithmic partial derivatives extend the results of Gundersen \cite{GG2} to the…
A crucial ingredient in the recent discovery by Ablowitz, Halburd, Herbst and Korhonen \cite{AHH}, \cite {HK-2} that a connection exists between discrete Painlev\'e equations and (finite order) Nevanlinna theory is an estimate of the…
The existence of meromorphic solutions to various difference equations has been extensively studied in recent years, the precise functional forms of such solutions -- particularly when the function and its difference operators share values…
This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic function, holds. Second, a difference analogue of logarithmic…
The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type…
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 are integers at every point. These functions…
The purpose of this article is threefold. The first is to construct a Nevanlina theory for meromorphic mappings from a polydisc to a compact complex manifold. In particular, we give a simple proof of Lemma on logarithmic derivative for…
In this paper, we study $q$-difference analogues of several central results in value distribution theory of several complex variables such as $q$-difference versions of the logarithmic derivative lemma, the second main theorem for…
By extending the idea of a difference operator with a fixed step to varying-steps difference operators, we have established a difference Nevanlinna theory for meromorphic functions with the steps tending to zero (vanishing period) and a…
By using Nevanlinna theory, we prove some normality criteria for a family of meromorphic functions under a condition on differential polynomials generated by the members of the family.
In this paper, we investigate shared value problems for shifts and higher-order difference operators of meromorphic and entire functions in several complex variables. Using Nevanlinna theory in $\mathbb{C}^n$, we obtain new uniqueness…
Certain estimates involving the derivative $f\mapsto f'$ of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose of this study is to extend the usual Nevanlinna theory to a…
The existence of the meromorphic solutions to Fermat type delay-differential equation \begin{equation} f^n(z)+a(f^{(l)}(z+c))^m=p_1(z)e^{a_1z^k}+p_2(z)e^{a_2z^k}, \nonumber \end{equation} is derived by using Nevanlinna theory under certain…
A two-parameter characteristic of functions meromorphic on annuli is introduced and an extension of the Nevanlinna value distribution theory for such functions is proposed.
In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…
For two meromorphic functions $ f $ and $ g $, the equation $ f^m+g^m=1 $ can be regarded as Fermat-type equations. Using Nevanlinna theory for meromorphic functions in several complex variables, the main purpose of this paper is to…
Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference…
The main purpose of this article is concerned with the existence and the precise forms of the transcendental solutions of several refined versions of Fermat-type functional equations with polynomial coefficients in several complex variables…