将微分方程的边(初)值问题化为泛函驻(极)值问题的一种新途径

An New Method To Convert The Boundary (And Initial-Boundary Value) Problems of Differential Equations Into the Stationary (Exterme) Value Problems of A Functional

研究了变分学中的逆问题,通过“变积”概念的提出,给出一种新的将微分方程的边(初)值问题化为泛函驻(极)值问题的途径。作为应用的实例,本文还研究了三类典型方程的转化问题。

In this paper, the inverse problem in calculus of variations is studied. A new concept called variational integral is introduced and by use of which, a new method is obtained to convert the boundary value (and initial-boundary value) problems of differential equations into the stationary (exterme) value problems of a functional. As an example, the inverse problem corresponding to the three kinds of carronical differential equation is studied.