On entire solutions of certain type of nonlinear differential equations
On entire solutions of certain type of nonlinear differential equations
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DOI：
10.1017/s0004972700019845
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发表时间：
2001-12
期刊：
影响因子：
2.2
通讯作者：
Chung-Chun Yang
中科院分区：
文献类型：
--
作者：
Chung-Chun Yang
In this note, we shall study, via Nevanlinna's value distribution theory, the uniqueness of transcendental entire solutions of the following type of nonlinear differential equation: (*) L ( f ( z )) – p ( z ) f n ( z ) = h ( z ), where L ( f ) denotes a linear differential polynomial in f with polynomials as its co-efficients, p ( z ) a polynomial (≢ 0), h an entire function, and n an integer ≥ 3. We show that if the equation (*) has a finite order transcendental entire solution, then it must be unique, unless L ( f ) ≡ 0.
