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中文摘要：
针对线性时变系统格林函数理论与应用研究中尚存在的问题,本文比较系统地研究了微分方程的格林函数方法,给出了与偏微分方程格林公式相对应的公式;总结出特征解法与基本解法两种求解微分方程的格林函数法,并讨论了他们之间的等价关系;给出了求解弦自由振动方程两种确定初位移方法：即弦位移格林函数法与微分方程格林函数特征解法。这些研究对于补充完善线性时变系统理论、促进非平稳信号处理方法的发展具有重要理论意义和应用意义。
英文摘要：
In order to solve the problem of the Green’s theory in the linear time-varying system,this paper studies the Green’s fuinction for solving differential equations and proposes a formular corresponding to the Green’s equation for par-tial differential equations.Two algorithms based on the Green’s function for solving the differential equation are summa-rized,including the eigen-value based algorithm and the fundamental algoithm.Their equivalence for both algorithms are also discussed.Furthermore,two methods to determine the initial displacement for a free string vibration equation are pres-ented,i.e.the Green’s function based string displacement method and the eigen-value of the differential equation besed Green’s function method.These results are very important in theory and applications for the development of the theory on the linear time-varying system and non-stationary signal processing.
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