微分方程f″+e^{az}f′+Q(z)f=F(z) 的复振荡

Abstract

Abstract:

The authors investigated the complex oscillation of different ial equations f″+e^{az}f′+Q(z)f=F(z), where Q(z)、F(z)(0) being entire functions and σ(Q)=1, σ(F)<+∞,where Q(z)=h(z)e^{bz},h(z) being a nonzero polynomial and b≠-1 being a complex constant, then all solutions f(z) of the above equation s satisfy ~λ(f)=λ(f)=σ(f)=∞,~λ_2(f)=λ_2(f)=σ_2(f)=1.except at most two exceptional complex numbers and one exceptional solution f_0(z) with finite order.

Key words: Differential equations,Order of growth,Exponent of convergence

CLC Number:

30D35

Cite this article

LI Chun-Gong, GU Yong-Xin. On the Complex Oscillation of Differential Equations f″+e^{az}f′+Q(z)f=F(z)[J].Acta mathematica scientia,Series A, 2005, 25(2): 192-200.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbA/EN/

http://121.43.60.238/sxwlxbA/EN/Y2005/V25/I2/192

Trendmd

References

[1] 杨乐. 值分布论及其新研究，北京:科学出版社， 1982

[2]高仕安,陈宗煊,陈特为. 线性微分方程的复振荡理论. 武汉: 华中科技大学出版社，1997

[3] 何育赞,萧修治. 代数体函数与常微分方程. 北京: 科学出版社，1988

[4]仪洪勋,杨重骏. 亚纯函数唯一性理论. 北京: 科学出版社，1995

[5] Chen Z X, Yang C C.Some further results on the zeros and growths of entire solutions of second order linear differential equations.Kodai Math J, 1999, 22: 273-285

[6]陈宗煊. 关于微分方程解的增长性. 中国科学（Ａ辑），2001,9:775- 784

[7]Frei M.Uberdie subnormaen losungen der differentialgleichung Ω;″e^{-z}Ω;′K const.Ω=0.Comment Math Helv, 1962, 36: 1-8

[8]Ozawa M. On a solution of Ω;″e^{-z}Ω;′(az+b)Ω=0. KodaiMath J,1980, 3:295- 309

[9]AmemiyaI, Ozawa M.Nonexistence of finite order solution of Ω;″e^{-z}Ω;′Q(z)Ω=0. Hokkaido Math J, 1981, 10:1-17

[10]Gundersen G.On the question of whether f″e^{-z}f′B(z)f=0,can admit a solution f(z)(0) of finite order. Proc RSE, 1986,102A: 9-17

[11]Langley J K.On complex oscillation and a problem of Ozawa. Kodai Math J, 1986, 9:430-439

[12]Chen Z X,Gao S A.The complex oscillation theory of certain nonhom ogeneous linear differential equations with transcendental entire coefficients.J Math Analy App, 1993, 179(2): 403-416

[13]Chen Z X.The zero、pole and order of meromorphic solution of differe ntial equations with meromorphic coefficients. Kodai Math J, 1996,19: 341-354

Related Articles 15

[1]	WANG Song-Min. On the Fundamental Theorems for Reducible Algebroid Functions [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1219-1227.
[2]	JIANG Yun-Bo, GAO Zong-Sheng. Uniqueness of Algebroid Functions Concerning CM Shared Values [J]. Acta mathematica scientia,Series A, 2014, 34(4): 796-801.
[3]	CHEN Jun-Fan. On the Growth of Meromorphic Functions in Some Angular Domains [J]. Acta mathematica scientia,Series A, 2014, 34(4): 1014-1025.
[4]	ZHANG Ke-Yu, YI Hong-Xun. THE VALUE DISTRIBUTION AND UNIQUENESS OF ONE CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS [J]. Acta mathematica scientia,Series A, 2014, 34(3): 719-728.
[5]	LU Qian, LIAO Qi-Long. Zeros of Differential Polynomials and Normal Criterions [J]. Acta mathematica scientia,Series A, 2014, 34(2): 317-326.
[6]	HUANG Wen, XIE Ya-Sheng . Normal Family of Holomorphic Functions [J]. Acta mathematica scientia,Series A, 2012, 32(6): 1166-1170.
[7]	QIU Jin-Di, LIN Xiu-Qing. Uniqueness of Meromorphic Functions whose Derivatives Share Four Values [J]. Acta mathematica scientia,Series A, 2012, 32(5): 964-973.
[8]	WANG Song-Min. The Relation between the Orders of Algebroid Functions and their Coefficients II [J]. Acta mathematica scientia,Series A, 2011, 31(6): 1647-1653.
[9]	LIU Hui-Fang, SUN Dao-Chun. Uniqueness Theorems for Algebroid Functions Sharing Values with Their Derivatives [J]. Acta mathematica scientia,Series A, 2011, 31(5): 1335-1344.
[10]	ZHANG Xiao-Mei, SUN Dao-Chun. Uniqueness of Algebroidal Functions [J]. Acta mathematica scientia,Series A, 2011, 31(4): 1133-1139.
[11]	ZHANG Xiao-Yu, CHEN Jun-Fan, LIN Wei-Chuan. Uniqueness of Meromorphic Functions Concerning Differential Polynomials [J]. Acta mathematica scientia,Series A, 2011, 31(2): 447-454.
[12]	TU Jin, DENG Guan-Tie. Growth of Solutions of Higher Order Linear Differential Equations with the Coefficient A₀ Being Dominant [J]. Acta mathematica scientia,Series A, 2010, 30(4): 945-952.
[13]	CHEN Yu. The Order, and \|Lower Order of Growth, and the Hyper-order of a Class of Higher Order Linear Differential Equations with Entire [J]. Acta mathematica scientia,Series A, 2010, 30(4): 1030-1041.
[14]	WU Zhao-Jun. Uniqueness Theorems of Meromorphic Functions in an Angular Domain [J]. Acta mathematica scientia,Series A, 2010, 30(3): 793-799.
[15]	LIU Hui-Fang, SUN Dao-Chun. On the Borel Direction Dealing with Multiple Values of Algebroidal Functions and Their Derivatives [J]. Acta mathematica scientia,Series A, 2009, 29(6): 1537-1546.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Wang Jinping. Some Results on the Exponential Radon Transform[J]. Acta mathematica scientia,Series A, 2006, 26(1): 31 -038 .
[2]	Su Hua; Liu Lishan; Wu Congxin. Iterative Solution for Systems of a Class of Abstract Operator Equations and Applications [J]. Acta mathematica scientia,Series A, 2007, 27(3): 449 -455 .
[3]	Luo Luo. Multipliers Between Hardy Spaces on the Unit Ball[J]. Acta mathematica scientia,Series A, 2007, 27(2): 204 -207 .
[4]	Tong Xiaojiao;He Bingsheng. An Inexact Alternating Direction Method for Solving a Class of Monotone Variational Inequalities [J]. Acta mathematica scientia,Series A, 2006, 26(2): 273 -282 .
[5]	Wang Qinlong; Liu Yirong. Isochronous Center for a Class of Quintic System[J]. Acta mathematica scientia,Series A, 2007, 27(6): 1044 -1053 .
[6]	Wei Zhongli. Positive Solutions of Some Singular Sub-linear Three-point Boundary Value Problems[J]. Acta mathematica scientia,Series A, 2008, 28(1): 174 -182 .
[7]	Yuan Baoquan. Remark on the Regular and Singular Solutions to Nonlinear Parabolic-elliptic System[J]. Acta mathematica scientia,Series A, 2008, 28(4): 627 -635 .
[8]	WANG Wei-Hong, WU Huo-Xiong. Weighted Weak Type Estimates for Commutators of \|Fractional Integrals on Spaces of Homogeneous Type[J]. Acta mathematica scientia,Series A, 2009, 29(3): 553 -563 .
[9]	GU Feng. On the Ishikawa Iterative Approximation with Mixed Errors for Solutions to Variational Inclusions with Strongly Accretive Type Mappings in Banach Spaces[J]. Acta mathematica scientia,Series A, 2005, 25(2): 176 -181 .
[10]	ZHI Hong-Yan, CHEN Yong, ZHANG Hong-Qing. Projective Riccati Equation Method and New Exact Travelling Wave Solutions for the (2+1)-dimensional Long Wave Equations[J]. Acta mathematica scientia,Series A, 2005, 25(7): 956 -964 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP

On the Complex Oscillation of Differential Equations f″+e^{az}f′+Q(z)f=F(z)

PDF (PC)