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ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS
Lu, Weiran,Li, Qiuying,Yang, Chungchun Korean Mathematical Society 2014 대한수학회보 Vol.51 No.5
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].
On the transcendental entire solutions of a class of differential equations
Weiran Lu,Qiuying Li,Chungchun Yang 대한수학회 2014 대한수학회보 Vol.51 No.5
In this paper, we consider the differential equation F′ − Q1 = Reα(F − Q2), where Q1 and Q2 are polynomials with Q1Q2 6≡ 0,R is a rational function and α is an entire function. We consider solutions of the form F = fn, where f is an entire function and n ≥ 2 is an integer, and we prove that if f is a transcendental entire function, then Q1 Q2 is a polynomial and f′ = Q1 nQ2 f. This theorem improves some known results and answers an open question raised in [16].