一类四阶椭圆型微分方程边值问题的边界变分方程

摘要

对一类四阶椭圆型微分方程边值问题给出解的存在唯一性定理并对内、外统一的边界积分方程与边界变分方程，证明了引入Lagrange乘子法的边界变分方程解的存在唯一性.%In this paper, a boundary value problem of a kind of four order elliptic differential equation is discussed by the Boundary Element Method. It is shown that the problems have one and only one solution.The boundary integral equation and boundary variation equation have been established, and the existence and uniqueness of the boundary variation equation are proved by using Lagrange multipliers defined in the boundary.