A variational principle for singular integral equations with bounded solutions

In many boundary value problems involving triple integral equations or triple series relations, it is required to solve a single singular integral equation with constant but unknown limits of integration. In this paper we present a variational method to determine approximately the bounded unknown function, if it exists, together with the unknown limits of integration for a type of such singular integral equations. The method is used to recover the exact solution of an integral equation and is applied to a contact problem in the theory of elasticity which is intractable otherwise.