ENTIRE SOLUTIONS TO FERMAT-TYPE DIFFERENCE AND PARTIAL DIFFERENTIAL-DIFFERENCE EQUATIONS IN Cn

被引：7

作者：

Xu, Hong Yan ^{[1
]}

Haldar, Goutam ^{[2
]}

机构：

[1] Suqian Univ, Sch Arts & Sci, Suqian 223800, Jiangsu, Peoples R China

[2] Ghani Khan Choudhury Inst Engn & Technol, Dept Math, Malda 732141, West Bengal, India

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 2024卷 / 26期

基金：

中国国家自然科学基金;

关键词：

Entire solutions; Fermat-type; partial differential equations; Nevanlinna theory; 2ND MAIN THEOREM; MEROMORPHIC SOLUTIONS; LEMMA;

D O I：

10.58997/ejde.2024.26

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the existence and the form of finite order transcendental entire solutions of systems of Fermat-type difference and partial differential-difference equations in several complex variables. Our results extend previous theorems given by Xu-Cao [49], Xu et al [52], and Zheng-Xu [55]. We give some examples to illustrate the content of this article.

引用

页数：21

共 56 条

[1] [Anonymous], 1964, Partial Differential Equations
[2] BIANCOFIORE A, 1981, ANN MATH STUD, P29
[3] A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables
Cao, Tingbin
Korhonen, Risto
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 444 (02) : 1114 - 1132
[4] On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane
Chiang, Yik-Man
Feng, Shao-Ji
[J]. RAMANUJAN JOURNAL, 2008, 16 (01) : 105 - 129
[5] Courant R., 1962, Methods of Mathematical Physics, V2
[6] ON EQUATION FN+GN=1
GROSS, F
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 72 (1P1) : 86 - &
[7] Gross F, 1956, Amer. Math. Monthly., V73, P1093
[8] Finite-order meromorphic solutions and the discrete Painleve equations
Halburd, R. G.
Korhonen, R. J.
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2007, 94 : 443 - 474
[9] Halburd RG, 2006, ANN ACAD SCI FENN-M, V31, P463
[10] Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations
Halburd, RG
Korhonen, RJ
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 314 (02) : 477 - 487

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