一类高阶周期线性微分方程解的性质

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国家自然科学基金资助项目

详细信息

On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations

摘要: 研究了一类高阶周期系数线性微分方程在其系数 $A_{1}$ 起控制作用时，方程\qquad \qquad \qquad \qquad $f^{(k)}+A_{k-2}f^{(k-2)}+\cdots+A_{1}f^{'}+A_{0}f=0$ 的解 $f(z)$ 和 $f(z+2\pi i)$ 的线性相关性.
- 周期系数 /
- 线性微分方程 /
- 线性无关
Abstract: The property of linearly dependence of solutions $f(z)$ and $f(z+2\pi \mathrm{i})$ for higher-order linear differential equations $f^{(k)}+A_{k-2}f^{(k-2)}+\cdots+A_{1}f^{'}+A_{0}f=0$ with periodic entire coefficients is investigated, where $A_{1}$ for the equation is the dominant coefficient.
- periodic coefficients /
- linearly differential equation /
- linearly independent