# ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS

• Lu, Weiran (Department of Mathematics China University of Petroleum) ;
• Li, Qiuying (Department of Mathematics China University of Petroleum) ;
• Yang, Chungchun (Department of Mathematics China University of Petroleum)
• Received : 2011.11.09
• Published : 2014.09.30

#### Abstract

In this paper, we consider the differential equation $$F^{\prime}-Q_1=Re^{\alpha}(F-Q_2)$$, where $Q_1$ and $Q_2$ are polynomials with $Q_1Q_2{\neq}0$, R is a rational function and ${\alpha}$ is an entire function. We consider solutions of the form $F=f^n$, where f is an entire function and $n{\geq}2$ is an integer, and we prove that if f is a transcendental entire function, then $\frac{Q_1}{Q_2}$ is a polynomial and $f^{\prime}=\frac{Q_1}{nQ_2}f$. This theorem improves some known results and answers an open question raised in [16].

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#### Cited by

1. A RESULT ON A CONJECTURE OF W. LÜ, Q. LI AND C. YANG vol.53, pp.2, 2016, https://doi.org/10.4134/BKMS.2016.53.2.411