On composition of meromorphic functions in several complex variables

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.

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Entire solutions for several second-order partial differential-difference equations of Fermat type with two complex variables

Advances in Difference Equations ◽

10.1186/s13662-020-03201-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Hong Yan Xu ◽

Da Wei Meng ◽

Sanyang Liu ◽

Hua Wang

Keyword(s):

Finite Order ◽

Difference Equations ◽

Nevanlinna Theory ◽

Meromorphic Functions ◽

Complex Variables ◽

Second Order ◽

Several Complex Variables ◽

Entire Solutions ◽

Partial Differential

AbstractThis paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference equations with more general forms of Fermat type. By utilizing the Nevanlinna theory of meromorphic functions in several complex variables we obtain some results on the forms of entire solutions for these equations, which are some extensions and generalizations of the previous theorems given by Xu and Cao (Mediterr. J. Math. 15:1–14, 2018; Mediterr. J. Math. 17:1–4, 2020) and Liu et al. (J. Math. Anal. Appl. 359:384–393, 2009; Electron. J. Differ. Equ. 2013:59–110, 2013; Arch. Math. 99:147–155, 2012). Moreover, by some examples we show the existence of transcendental entire solutions with finite order of such equations.

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The star function for meromorphic functions of several complex variables

Complex Variables and Elliptic Equations ◽

10.1080/17476933.2017.1410797 ◽

2017 ◽

Vol 64 (1) ◽

pp. 26-39

Author(s):

Faruk Abi-Khuzam ◽

Florian Bertrand ◽

Giuseppe Della Sala

Keyword(s):

Meromorphic Functions ◽

Complex Variables ◽

Several Complex Variables

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q-Differences theorems for meromorphic maps of several complex variables intersecting hypersurfaces

Asian-European Journal of Mathematics ◽

10.1142/s1793557121500406 ◽

2020 ◽

pp. 2150040

Author(s):

Pham Duc Thoan ◽

Nguyen Hai Nam ◽

Noulorvang Vangty

Keyword(s):

Growth Condition ◽

Meromorphic Functions ◽

Complex Variables ◽

Zero Order ◽

Several Complex Variables ◽

Meromorphic Mappings ◽

Meromorphic Maps

In this paper, we show some [Formula: see text]-difference analogues of the second main theorems for algebraically nondegenerate meromorphic mappings over the field [Formula: see text] of zero-order meromorphic functions in [Formula: see text] satisfying [Formula: see text] intersecting hypersurfaces, located in subgeneral position in [Formula: see text], where [Formula: see text] and [Formula: see text] may be different. As an application, we give some unicity theorems for meromorphic mappings of [Formula: see text] into [Formula: see text] under the growth condition “order [Formula: see text]”, which are analogous to Picard’s theorems.

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