系数是周期$2\pi i$的二阶复微分方程

Abstract

Abstract: In this paper, we mainly learned classic book 'Nevanlinna theory and complex differential equations' due to Laine and considered the second order complex differential equation $f '' + A (z) f=0, \lambda(f)<\infty$ with coefficient $A (z) $ whose period is $2 \pi i$. We found a possible error in the original proof and gave its partial correction, and also we gave a slightly weaker conclusion than its possibly controversial result in the original literature.

Key words: Complex differential equation, Nevanlinna theory, entire function, exponent of convergence for zero-sequence

CLC Number:

O174.5

Jie ZHANG. On second order complex differential equations with coefficients of period $2\pi i$[J].Acta mathematica scientia,Series A, , (): 0-0.

Trendmd

[1]	Shuqing Lin,Junfan Chen. The Non-Existence of Solutions of a Certain type of Nonlinear Complex Differential-Difference Equations [J]. Acta mathematica scientia,Series A, 2021, 41(1): 69-80.
[2]	Manli Liu,Lingyun Gao. Behaviour of Meromorphic Solutions of Complex Functional-Differential Equations [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1121-1131.
[3]	Wang Qiong, Hu Peichu. On Zeros and Periodicity of Entire Functions [J]. Acta mathematica scientia,Series A, 2018, 38(2): 209-214.
[4]	Lin Weichuan, Luo Xudan. On the Zeros of Confluent Hypergeometric Functions [J]. Acta mathematica scientia,Series A, 2017, 37(5): 801-807.
[5]	Wang Yue, Gao Lingyun. On the Behavior of Systems of Complex Difference Equations with Admissible Solutions [J]. Acta mathematica scientia,Series A, 2016, 36(5): 901-910.
[6]	Chen Shengjiang. Further Results on Periodicity and Unicity of Entire Functions [J]. Acta mathematica scientia,Series A, 2016, 36(5): 911-918.
[7]	Chen Minfeng, Gao Zongsheng. Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equation [J]. Acta mathematica scientia,Series A, 2016, 36(2): 297-306.
[8]	WANG Yue, ZHANG Qiang-Cai, YANG Ming-Hua. The Growth of Solutions of Systems of Complex Difference-Differential Equations [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1337-1347.
[9]	SUN Gui-Rong. Oscillation Theory of Solution of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficient [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1426-1434.
[10]	WANG Yue, ZHANG Qiang-Cai. Solutions of Some Types of Systems of Complex Higher-Order q-Shift Difference Equations [J]. Acta mathematica scientia,Series A, 2014, 34(4): 761-768.
[11]	TAN Wei-Ping, ZHAN Xiao-Ping. The Exceptional Set for the Differential Polynomials of a Class of Slowly Growing Meromorghic Function [J]. Acta mathematica scientia,Series A, 2013, 33(4): 728-734.
[12]	LONG Jian-Ren, ZHU Jun, LI Xiao-Man. On the Growth of Solutions of Some Higher Order Linear Differential Equations [J]. Acta mathematica scientia,Series A, 2013, 33(3): 401-408.
[13]	SHENG Bao-Huai. The Weighted Norm for Some Mercer Kernel [J]. Acta mathematica scientia,Series A, 2013, 33(1): 6-15.
[14]	WU Xiu-Bi, WU Peng-Cheng. On the Growth of Solutions of f''+Af'+Bf=0, Where A is a Solution of a Second Order Linear Differential Equation [J]. Acta mathematica scientia,Series A, 2013, 33(1): 46-52.
[15]	WU Zhao-Jun, CHEN Yu-Xian. The Fixed Points of Solutions of Some Second Order Differential Equation [J]. Acta mathematica scientia,Series A, 2012, 32(4): 779-784.

On second order complex differential equations with coefficients of period $2\pi i$

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0