Entire Solutions of Two Certain Types of Non-linear Differential-Difference Equations

被引：9

作者：

Chen, Wei ^{[1
]}

Hu, Peichu ^{[2
]}

Wang, Qiong ^{[1
]}

机构：

[1] Chongqing Univ Posts & Telecommun, Sch Sci, Chongqing 400065, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2021年 / 21卷 / 02期

关键词：

Entire solution; Non-linear differential-difference equations; Nevanlinna theory; TUMURA-CLUNIE; THEOREM;

D O I：

10.1007/s40315-020-00343-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we describe entire solutions for two certain types of non-linear differential-difference equations of the form f(n)(z) + omega f(n-1) (z) f' (z) + q(z)e(Q(z)) f (z + c) = u(z)e(v(z)), and f(n)(z) + omega f(n-1) (z) f' (z) + q(z)e(Q(z)) f (z + c) = p(1)e(lambda z) + p(2)e(-lambda z), where q, Q, u, v are non-constant polynomials, c, lambda, p(1), p(2) are non-zero constants, and. is a constant. Our results improve and generalize some previous results.

引用

页码：199 / 218

页数：20

共 22 条

[1]

17Reyzl I., 1995, Complex Var. Theory Appl., V28, P175

[2] The Separation of Zeros of Solutions of Higher Order Linear Differential Equations With Entire Coefficients [J].

Alotaibi, Abdullah ;

Langley, J. K. .

RESULTS IN MATHEMATICS, 2013, 63 (3-4) :1365-1373

[3] Entire Solutions of Certain Type of Non-Linear Difference Equations [J].

Chen, Min-Feng ;

Gao, Zong-Sheng ;

Zhang, Ji-Long .

COMPUTATIONAL METHODS AND FUNCTION THEORY, 2019, 19 (01) :17-36

[4] On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane [J].

Chiang, Yik-Man ;

Feng, Shao-Ji .

RAMANUJAN JOURNAL, 2008, 16 (01) :105-129

[5]

Clunie J., 1962, J. Lond. Math. Soc, V37, P17, DOI DOI 10.1112/JLMS/S1-37.1.17

[6]

Halburd RG, 2006, ANN ACAD SCI FENN-M, V31, P463

[7] Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations [J].

Halburd, RG ;

Korhonen, RJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 314 (02) :477-487

[8]

Hayman W. K., 1964, MEROMORPHIC FUNCTION

[9]

Laine I., 2011, NEVANLINNA THEORY CO

[10] On the nonexistence of entire solutions of certain type of nonlinear differential equations [J].

Li, Ping ;

Yang, Chung-Chun .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 320 (02) :827-835

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