泛函建立方法的研究──变积方法

study on the method establishing functional-the method of variational integral

在变分学中，存在两类互道的问题，一类是将泛函的驻（极）值问题化为微分方程的边（初）值问题（正问题），一类是将微分方程的边（初）值问题化为泛函的驻（极）值问题（逆问题）．本文研究变分学中的逆问题．首先建立了变分的逆运算—变积的概念，然后应用变积运算顺利地将数理方法中的三类典型方程的边（初）值问题化为泛函的驻（极）值问题．

This paper study on the inverse problem in the calculus of variation. In the first place it establishes inverse calculation of variation-the concept of variational integral and then transforms the problem of boundary(initial)value of three kinds typical equations in the mathematical method into the problem of stationary(extreme)value of functional.