Transcendental entire solutions for several quadratic binomial and trinomial PDEs with constant coefficients

被引：30

作者：

Xu, Hong Yan ^{[1
,2
]}

Xu, Ling ^{[3
]}

机构：

[1] Gannan Normal Univ, Key Lab Jiangxi Prov Numer Simulat & Emulat Tech, Ganzhou 341000, Jiangxi, Peoples R China

[2] Shangrao Normal Univ, Sch Math & Comp Sci, Shangrao 334001, Jiangxi, Peoples R China

[3] Jiangxi Sci & Technol Normal Univ, Sch Math & Comp, Nanchan 330038, Jiangxi, Peoples R China

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Nevanlinna theory; Entire solution; Partial differential difference equation; EQUATIONS; THEOREM;

D O I：

10.1007/s13324-022-00679-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with the description of the existence of entire solutions of several quadratic binomial and trinomial partial differential equations (PDEs) with constant coefficients. We established a series of theorems on the forms of finite order transcendental entire solutions for such PDEs, which are some generalization and improvement of the previous theorems given by Cao, Liu, Xu and Yang (An Stiint Univ Al I Cuza Iasi Mat (NS) 1:317-325, 2016; Mediterr J Math 15:1-14, 2018; Mediterr J Math 17:1-4, 2020). Moreover, a series of examples are given to show that the existence conditions and the forms of transcendental entire solutions with finite order of such equations are precise.

引用

页数：21

共 28 条

[11] Entire solutions of certain partial differential equations and factorization of partial derivatives
Li, BQ
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (08) : 3169 - 3177
[12] On entire solutions of Fermat type partial differential equations
Li, BQ
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2004, 15 (05) : 473 - 485
[13] Liu K., 2016, An. Stiint. Univ. Al. I. Cuza Lasi Mat. (N. S.), V1, P317
[14] Meromorphic solutions of generalized inviscid Burgers' equations and related PDES
Lu, Feng
[J]. COMPTES RENDUS MATHEMATIQUE, 2020, 358 (11-12) : 1169 - 1178
[15] Growth and Uniqueness Related to Complex Differential and Difference Equations
Lue, Feng
Lue, Weiran
Li, Cuiping
Xu, Junfeng
[J]. RESULTS IN MATHEMATICS, 2019, 74 (01)
[16] Montel P., 1927, Lecons sur les familles de nomales fonctions analytiques et leurs applications, P135
[17] Polya G., 1926, J. Lond. Math. Soc., V1, P12
[18] Ronkin L.I., 1974, INTRO THEORY ENTIRE, V44, DOI [10.1090/mmono/044, DOI 10.1090/MMONO/044]
[19] Saleeby E.G., 2004, Complex Variables, Theory and Application: An International Journal, V49, P101
[20] Saleeby EG., 1999, Analysis, V19, P369

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