On Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations

被引：0

作者：

Xiao Qing LU ^{[1
]}

Liang Wen LIAO ^{[2
]}

Jun WANG ^{[3
]}

机构：

[1] Mathematics and Information Technology School, Jiangsu Second Normal University

[2] Department of Mathematics, Nanjing University

[3] School of Mathematical Sciences, Fudan University

来源：

Acta Mathematica Sinica,English Series | 2017年 / 12期

基金：

上海市自然科学基金;

关键词：

Meromorphic solutions; nonlinear differential equations; small functions; Nevanlinna’s value distribution theory;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

We consider transcendental meromorphic solutions with N（r,f） = S（r,f） of the following type of nonlinear differential equations:f+ Pn-2（f） = p1（z）e+p2（z）e,where n≥ 2 is an integer, Pn-2（f） is a differential polynomial in f of degree not greater than n-2 with small functions of f as its coefficients, p1（z）, p2（z） are nonzero small functions of f, and α1（z）, α2（z）are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of meromorphic solutions and their possible forms of the above equation. Our results extend and improve some known results obtained most recently.

引用

页码：1597 / 1608

页数：12

共 4 条

[1] Entire solutions of certain type of differential equations
Ping Li
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (01) : 253 - 259
[2] On the nonexistence of entire solutions of certain type of nonlinear differential equations[J] . Ping Li,Chung-Chun Yang.Journal of Mathematical Analysis and Applications . 2005 (2)
[3] On the transcendental solutions of a certain type of nonlinear differential equations
Yang, CC
Li, P
[J]. ARCHIV DER MATHEMATIK, 2004, 82 (05) : 442 - 448
[4] On meromorphic solutions of certain type of non-linear differential equations .2 Liao Liangwen,Yang Chungchun,Zhang Jianjun. Ann Acad Sci Fenn Math . 2013

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