| 一类高阶周期微分方程的解和小函数的关系 |
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| 引用本文： | 王青,陈宗煊.一类高阶周期微分方程的解和小函数的关系[J].华南师范大学学报(自然科学版),2013,45(3):16-21. |
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| 作者姓名： | 王青 陈宗煊 |
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| 作者单位： | 1.华南师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金项目(11171119) |
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| 摘 要： | 研究了微分方程~$f^{(k)}+P_{k-1}(\mathrm{e}^{z})+Q_{k-1}(\mathrm{e}^{-z})]f^{(k-1)}+\cdots+P_{0}(\mathrm{e}^{z})+Q_{0}(\mathrm{e}^{-z})]f=0$和 ~$f^{(k)}+P_{k-1}(\mathrm{e}^{z})+Q_{k-1}(\mathrm{e}^{-z})]f^{(k-1)}+\cdots+P_{0}(\mathrm{e}^{z})+Q_{0}(\mathrm{e}^{-z})]f=R_{1}(\mathrm{e}^{z})+R_{2}(\mathrm{e}^{-z})$~的解以及它们的一阶导数与小函数的关系, 其中~$P_{j}(z)$~,~$Q_{j}(z)$~$(j=0，1,2，\cdots，k-1)$~和~$R_{i}(z)(i=1，2)$~是关于~z~的多项式.
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| 关 键 词： | 收敛指数. |
| 收稿时间： | 2011-12-31 |
The Relation Between Solutions of a class of HigherOrder Differential Equations With Periodic Coefficients andFunctions of Small Growth |
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| WANG Qing,CHEN Zongxuan.The Relation Between Solutions of a class of HigherOrder Differential Equations With Periodic Coefficients andFunctions of Small Growth[J].Journal of South China Normal University(Natural Science Edition),2013,45(3):16-21. |
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| Authors: | WANG Qing CHEN Zongxuan |
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| Institution: | (School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China) |
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| Abstract: | Linear differential equations ~$f^{(k)}+P_{k-1}(\mathrm{e}^{z})+Q_{k-1}(\mathrm{e}^{-z})]f^{(k-1)}+\cdots+P_{0}(\mathrm{e}^{z})+Q_{0}(\mathrm{e}^{-z})]f=0$~and ~$f^{(k)}+P_{k-1}(\mathrm{e}^{z})+Q_{k-1}(\mathrm{e}^{-z})]f^{(k-1)}+\cdots+P_{0}(\mathrm{e}^{z})+Q_{0}(\mathrm{e}^{-z})]f=R_{1}(\mathrm{e}^{z})+R_{2}(\mathrm{e}^{-z})$~ where ~$P_{j}(z)$~,~$Q_{j}(z)$~$(j=0，1,2，\cdots，k-1)$~and~$R_{i}(z)(i=1，2)$~are polynomials in z are investigated. The relationship between solutions and their 1th derivatives and small functions are studied. |
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