| 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.
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| 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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.04.005 |
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