具有缺项级数系数的高阶齐次线性微分方程解的性质

Abstract

Abstract:

In the paper, the authors investigate the exponent of convergence of the zero-sequence of meromorphic solutions to homogeneous linear differential equation f^(k)+A_k_-2f^(k-2)+…+A₁f'+A₀f=0 when its coefficients are meromorphic functions possessing only a finite number of poles and dominant coefficient A_s(s∈{2, …, k-2}) is fabry gap. The minimum number of linear independent transcendental solutions and the maximum number of linear independ ent transcendental solutions with finite exponents of convergence of the zero-sequence are obtained.

Key words: Differential equation, Fabry gap, Linearly independent, Exponent of convergence of zero-sequence

CLC Number:

30D35

Cite this article

CHEN Mei-Ru, CHEN Zong-Xuan. The Properties of Solutions to Higher-order Homogeneous Linear Differential Equations with Coefficient of Fabry Gap[J].Acta mathematica scientia,Series A, 2011, 31(6): 1697-1707.

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/Y2011/V31/I6/1697

Trendmd

References

[1] 杨乐. 值分布论及其新研究. 北京: 科学出版社, 1982

[2] 仪洪勋, 杨重骏. 亚纯函数的唯一性理论. 北京: 科学出版社, 1995

[3] Barry P D. On a theorem of besicoivitch. Quart J Math Oxford, 1963, 14(2): 293--302

[4] Gao S A. Some results on the complex oscillation for higher order homogeneous linear differential equations. Kodai Math J, 1996, 19: 355--364

[5] 陈宗煊. 慢增长系数齐次线性微分方程解的性质. 江西师范大学学报(自然科学版), 1999, 23(4): 283--288

[6] Gundersen G. Estimates for the logarithmic derivative of a merommorphic function, plus similar estimates. J London Math Soc, 1988, 37(2): 88--104

[7] Tohge K. On the complex of some linear differential equation. Journal of Mathematical Analysis and Applications, 1997, 206: 503--517

[8] Sons L R. Analogue of a theorem of W.H.J.Fuchs on gap series. Proc Lon Math Soc, 1970, 21(3): 525--539

[9] 陈宗煊. 二阶亚纯系数微分方程亚纯解的零点. 数学物理学报,1996, 16(3): 276--283

[10] 高仕安, 陈宗煊, 陈特为. 线性微分方程的复振荡理论. 武汉: 华中理工大学出版社,1997

[11] Chen Z X, Shon K H. On the growth of solutions of a class of higher order differential equations. Acta Math Sci, 2004, 24B: 52--60

[12] 涂金, 陈宗煊. 一类高阶微分方程解的增长性. 数学物理学报, 2008, 28A(4): 670--678

Related Articles 15

[1]	Wang Huiwen, Zeng Hongjuan, Li Fang. An Existence Result for Impulsive Boundary Value Problem for Fractional Differential Equations with Multiple Base Points [J]. Acta mathematica scientia,Series A, 2018, 38(4): 697-715.
[2]	Zhang Xiaojian. Oscillation of Generalized Emden-Fowler Differential Equations with Nonlinear Neutral Term [J]. Acta mathematica scientia,Series A, 2018, 38(4): 728-739.
[3]	Wang Huiling, Gao Jianfang. Oscillation Analysis of Analytical Solutions for a Kind of Nonlinear Neutral Delay Differential Equations with Several Delays [J]. Acta mathematica scientia,Series A, 2018, 38(4): 740-749.
[4]	Wang Wansheng, Zhong Peng, Zhao Xinyang. Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay [J]. Acta mathematica scientia,Series A, 2018, 38(1): 96-109.
[5]	Li Wenjuan, Tang Huo, Yu Yuanhong. Oscillation of the Neutral Emden-Fowler Differential Equation [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1062-1069.
[6]	Xiong Jun, Li Junmin, He Chao. Fuzzy Boundary Control Design for a Class of First-Order Hyperbolic PDEs [J]. Acta mathematica scientia,Series A, 2017, 37(3): 469-477.
[7]	Wang Yunzhu, Gao Jianfang. Oscillation Analysis of Numerical Solutions in the θ-Methods for a Kind of Nonlinear Delay Differential Equation [J]. Acta mathematica scientia,Series A, 2017, 37(2): 342-351.
[8]	Chen Huiwen, Li Jianli, Shen Jianhua. New Results for Neumann Boundary Value Problem with Impulses via Variational Methods [J]. Acta mathematica scientia,Series A, 2017, 37(1): 54-61.
[9]	Zeng Yunhui, Luo Liping, Yu Yuanhong. Oscillation Criteria for Generalized Neutral Emden-Fowler Equations [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1067-1081.
[10]	Liu Hongying, Lv Xueqin. Method for Solving a Class of Fourth Order Nonlinear Differential Equations with Integral Boundary Conditions by Combining Collocation Method and Reproducing Kernel Method [J]. Acta mathematica scientia,Series A, 2016, 36(5): 928-936.
[11]	Marko Kostić, Li Chenggang, Li Miao. Abstract Multi-Term Fractional Differential Equations with Riemann-Liouville Derivatives [J]. Acta mathematica scientia,Series A, 2016, 36(4): 601-622.
[12]	Yao Qingliu. Existence and Successively Iterative Method of Singular Solution to a Nonlinear Fractional Differential Equation [J]. Acta mathematica scientia,Series A, 2016, 36(2): 287-296.
[13]	Feng Yuqiang, Wang Weimin, Li Shougui. Existence and Uniqueness Results for the Periodic Boundary Value Problems of Fractional Differential Equations with Singular Nonlinearities [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1059-1070.
[14]	Liangquan Zhang. The Viability Property for Path-Dependent SDE Under Open Constraints [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1168-1179.
[15]	Wei Li, Agarwal Ravi P. Monotonicity Method for Hyperbolic Type Nonlinear Differential Equation with Generalized p-Laplacian [J]. Acta mathematica scientia,Series A, 2015, 35(5): 867-877.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Gong Xiaoqing. Statistical Analysis on Evolutionary Behaviors of Games[J]. Acta mathematica scientia,Series A, 2006, 26(5): 747 -752 .
[2]	Ren Han; Deng Mo; Lu Junjie. Near-trangular Embeddings for Triangulations of the Sphere and the Torus (I) [J]. Acta mathematica scientia,Series A, 2006, 26(2): 207 -211 .
[3]	Zhuang Yan;Dai Chaoshou. The Hausdorff Dimension for a Class of Generalized Random Fractals[J]. Acta mathematica scientia,Series A, 2008, 28(2): 240 -250 .
[4]	LibingHuang ; Mo Xiaohuan. On the Construction of {\boldmath $p$}-harmonic Morphisms[J]. Acta mathematica scientia,Series A, 2008, 28(2): 232 -239 .
[5]	XU Li-Wen, WANG Song-Gui. The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models[J]. Acta mathematica scientia,Series A, 2009, 29(2): 223 -232 .
[6]	Chen Huanyin. A Note on Strongly Separativity over Exchange Rings[J]. Acta mathematica scientia,Series A, 2009, 29(2): 378 -382 .
[7]	MENG Beng-Hua. Relation Between Power Lattice and Quotient Lattice [J]. Acta mathematica scientia,Series A, 2004, 24(4): 491 -495 .
[8]	WANG Hai-Bin, HUI Bo-Cheng, CHEN Gao-Qiu. The Approximate Third order Moments and Bispectral Density of LTBL Model[J]. Acta mathematica scientia,Series A, 2004, 24(4): 501 -512 .
[9]	FANG Shao-Mei, GUO BO-Ling. Attractors for a Damped Generalized Coupled Nonlinear Wave Equations in an Unbounded Domain[J]. Acta mathematica scientia,Series A, 2003, 23(4): 464 -473 .
[10]	PENG Yan-Fang, ZHANG Zheng-Jie. Existence of Solution for a \|Singular Biharmonic Equation Involving Critical Exponent[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1492 -1499 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP

The Properties of Solutions to Higher-order Homogeneous Linear Differential Equations with Coefficient of Fabry Gap

PDF (PC)