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Growth of solutions of a class of complex differential equations

100%
Cao T.-B.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 2
141-152
EN
The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359-370] by proving that every entire solution f of the differential equation $f'-e^{P(z)}f = 1$ has infinite order and its hyperorder is a positive integer or infinity, where P is a nonconstant entire function of order less than 1/2. As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21-24].
2
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Analytic functions in the unit disc sharing values in a sector

64%
Xu H.-Y., Cao T.-B.
Annales Polonici Mathematici
|
2012
|
tom 103
|
nr 3
263-275
EN
We deal with the uniqueness of analytic functions in the unit disc sharing four distinct values and obtain two theorems improving a previous result given by Mao and Liu (2009).
3
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Uniqueness of two analytic functions sharing four values in an angular domain

64%
Xu H.-Y., Cao T.-B.
Annales Polonici Mathematici
|
2010
|
tom 99
|
nr 1
55-65
EN
We deal with the uniqueness problem for analytic functions sharing four distinct values in an angular domain and obtain some theorems which improve the result given by Cao and Yi [J. Math. Anal. Appl. 358 (2009)].
4
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Solutions of non-homogeneous linear differential equations in the unit disc

64%
Cao T.-B., Deng Z.-S.
Annales Polonici Mathematici
|
2010
|
tom 97
|
nr 1
51-61
EN
The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $f^{(k)} + a_{k-1}(z)f^{(k-1)} + ⋯ + a₁(z)f' + a₀(z)f = F(z)$, where all coefficients $a₀,a₁,...,a_{k-1}$, F ≢ 0 are analytic functions in the unit disc 𝔻 = {z∈ℂ: |z|<1}. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.
5
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Multiple values and uniqueness problem for meromorphic mappings sharing hyperplanes

51%
Cao T.-B., Liu K., Cao H.-Z.
Annales Polonici Mathematici
|
2013
|
tom 107
|
nr 2
153-166
EN
The purpose of this article is to deal with multiple values and the uniqueness problem for meromorphic mappings from $ℂ^{m}$ into the complex projective space ℙⁿ(ℂ) sharing hyperplanes. We obtain two uniqueness theorems which improve and extend some known results.
6
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Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight

51%
Xu H.-Y., Yi C.-F., Cao T.-B.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 1
51-66
EN
This paper deals with the uniqueness problem for meromorphic functions sharing one value with finite weight. Our results generalize those of Fang, Hong, Bhoosnurmath and Dyavanal.
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