一种第一类Fredholm积分方程组解的存在唯一性的充分必要条件

The necessary and sufficient condition for the existence and uniqueness of a system of Fredholm integral equations of the first kind

本文研究由二维多连通区域上Laplace方程Dirichlet问题产生的第一类Fredholm积分方程组解的存在唯一性;引进了一个判别指标γN,它是可计算的;证明了此第一类Fredholm积分方程组解的存在唯一性的充分必要条件为γN≠0;并通过数值例子验证了本文的理论结果.

In this paper, we consider the existence and uniqueness of a system of Fredholm integral equations of the first kind, which arises from the Dirichlet problem for Laplace equation on 2D multiply-connected domains. We introduce a computable index γN and prove that the necessary and sufficient condition for the existence and uniqueness of solution of this Fredholm integral equations of the first kind is γN ≠ 0. The numerical examples demonstrate the validity of our theoretic results.