Taiwanese Journal of Mathematics

ON ENTIRE SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR DIFFERENTIAL AND DIFFERENCE EQUATIONS

Jie Zhang and Liang-Wen Liao

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Abstract

In this paper, we investigate some analogous results on the existence of entire solutions of a certain type of nonlinear differential and differential-difference equations of the following form $$ f^n(z) + P_d(f) = p_1(z) e^{\alpha_1 z} + p_2(z) e^{\alpha_2 z},$$ where $P_d(f)$ is a differential polynomial or differential-difference polynomial in $f(z)$. And we find out its entire solutions or prove that it has no entire solution for some special $P_d(f)$.

Article information

Source
Taiwanese J. Math., Volume 15, Number 5 (2011), 2145-2157.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406427

Digital Object Identifier
doi:10.11650/twjm/1500406427

Mathematical Reviews number (MathSciNet)
MR2880397

Zentralblatt MATH identifier
1242.30025

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 34M10: Oscillation, growth of solutions

Keywords
differential polynomial differential-difference polynomial small function entire order

Citation

Zhang, Jie; Liao, Liang-Wen. ON ENTIRE SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR DIFFERENTIAL AND DIFFERENCE EQUATIONS. Taiwanese J. Math. 15 (2011), no. 5, 2145--2157. doi:10.11650/twjm/1500406427. https://projecteuclid.org/euclid.twjm/1500406427


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