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http://dx.doi.org/10.4134/BKMS.2014.51.5.1281

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.5, 2014 , pp. 1281-1289 More about this Journal
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].
Keywords
transcendental entire solutions; differential equation; Nevanlinna theory;
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Times Cited By KSCI : 2  (Citation Analysis)
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