一类常微分方程边值问题的格林函数的讨论

Discussion on Green Function for a Class of Boundary Value Problems of Ordinary Differential Equations

为了研究方便,通常应用格林函数将微分方程转化为与其等价的积分方程。通过常数变易法研究了一类三阶常微分方程在一类边值条件下的格林函数求法,也给出了另一类边值条件下微分方程的格林函数表达式,最后给出了一些上述方程求解格林函数的实例。

In order to study conveniently, the differential equation is transformed into its equivalent integral e- quation by using Green~ function. The Green function for a third - order ordinary differential equation with a boundary condition was studied by the method of variation of constant. The expression of the Green function for other boundary condition was also given. Finally some examples of Green function were provided for boundary value problems of ordinary differential equations.