Taiwanese Journal of Mathematics

ON ENTIRE SOLUTIONS OF CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE EQUATIONS

Zong-Xuan Chen and Chung-Chun Yang

Full-text: Open access

Abstract

In this paper, we deal with differential-difference equations of the form $$ f(z)^2+p(z)f(z+c)+h(z)f'(z)+g(z)=d_1e^{\lambda z}+d_2e^{-\lambda z} $$ where $p(z),~ h(z),~ g(z)$ are polynomials, and $c,~ d_1,~d_2, ~\lambda\in \mathbb{C}$ are constants with $d_1 d_2\lambda\not= 0$. By utilizing Nevanlinna's value distribution theory, some sufficient conditions on the nonexistence of entire solutions regarding the equations are provided.

Article information

Source
Taiwanese J. Math., Volume 18, Number 3 (2014), 677-685.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706433

Digital Object Identifier
doi:10.11650/tjm.18.2014.3745

Mathematical Reviews number (MathSciNet)
MR3213379

Zentralblatt MATH identifier
1357.30020

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 39A10: Difference equations, additive

Keywords
Nevanlinna theory differential-difference polynomial entire solution

Citation

Chen, Zong-Xuan; Yang, Chung-Chun. ON ENTIRE SOLUTIONS OF CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE EQUATIONS. Taiwanese J. Math. 18 (2014), no. 3, 677--685. doi:10.11650/tjm.18.2014.3745. https://projecteuclid.org/euclid.twjm/1499706433


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