ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS

Title & Authors
ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS
Lu, Weiran; Li, Qiuying; Yang, Chungchun;

Abstract
In this paper, we consider the differential equation $\small{F^{\prime}-Q_1=Re^{\alpha}(F-Q_2)}$, where $\small{Q_1}$ and $\small{Q_2}$ are polynomials with $\small{Q_1Q_2{\neq}0}$, R is a rational function and $\small{{\alpha}}$ is an entire function. We consider solutions of the form $\small{F=f^n}$, where f is an entire function and $\small{n{\geq}2}$ is an integer, and we prove that if f is a transcendental entire function, then $\small{\frac{Q_1}{Q_2}}$ is a polynomial and $\small{f^{\prime}=\frac{Q_1}{nQ_2}f}$. This theorem improves some known results and answers an open question raised in [16].
Keywords
transcendental entire solutions;differential equation;Nevanlinna theory;
Language
English
Cited by
1.
A RESULT ON A CONJECTURE OF W. LÜ, Q. LI AND C. YANG,;

대한수학회보, 2016. vol.53. 2, pp.411-421
1.
A RESULT ON A CONJECTURE OF W. LÜ, Q. LI AND C. YANG, Bulletin of the Korean Mathematical Society, 2016, 53, 2, 411
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