EXISTENCE OF MEROMORPHIC SOLUTIONS OF SOME HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(13)60023-5

Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (2): 600-608.doi: 10.1016/S0252-9602(13)60023-5

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EXISTENCE OF MEROMORPHIC SOLUTIONS OF SOME HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

ZHANG Xiao-Mei, SUN Dao-Chun

Basic Teaching Department, Guangzhou Civil Aviation College, Guangzhou 510403, China； School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received:2010-06-18 Revised:2011-01-10 Online:2013-03-20 Published:2013-03-20
Supported by:
This research is supported by the National Natural Science Foundation of China (11101096).

This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic
solutions of linear differential equations.

Key words: Higher order linear differential equation, meromorphic coefficient, meromorphic solutions, the first coefficient

CLC Number:

30D35

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ZHANG Xiao-Mei, SUN Dao-Chun. EXISTENCE OF MEROMORPHIC SOLUTIONS OF SOME HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS[J].Acta mathematica scientia,Series B, 2013, 33(2): 600-608.

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[2] Wang R H, Wu Z Q. Lecture of ordinary differential equation. Beijing: People’s Education Press, 1963 (in Chinese)

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[4] Bank S B. On the existence of meromorphic solutions of differential equations having arbitrarily rapid growth. J Reine Angew Math, 1976, 288: 176–182

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EXISTENCE OF MEROMORPHIC SOLUTIONS OF SOME HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

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