On the Property of Solutions for a Class of Higher Order Periodic Differential Equations
Received:February 01, 2012  Revised:November 22, 2012
Key Words: differential equation   linearly dependent   periodic coefficients.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11126144; 11171119), the Youth Science Foundation of Education Bureau of Jiangxi Province (Grant No.GJJ12207) and the Natural Science Foundation of Jiangxi Province (No.20132BAB211009).
Author NameAffiliation
Lipeng XIAO Institute of Mathematics and Information, Jiangxi Normal University, Jiangxi 330022, P. R. China 
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      In this paper, the property of linear dependence of solutions for higher order linear differential equation $$f^{(k)}(z)+A_{k-2}(z)f^{(k-2)}(z)+\cdots+A_0(z)f(z)=0,\eqno(*)$$ where $A_j(z)~(j=0,2,\ldots,k-2)$ are constants and $A_1$ is a non-constant entire function of period $2\pi i$ and rational in $e^z$, is investigated. Under certain condition, the representation of solution of Eq.\,$(*)$ is given, too.
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