Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions

Charles T. Fultona1

a1 Department of Mathematics, The Pennsylvania State University


In this paper it is shown that the analysis of Titchmarsh's book [32] for regular Sturm-Liouville problems on a finite closed interval carries over readily to regular problems involving the eigenvalue parameter in the boundary condition at one end-point. The manner in which this type of problem is associated with a self-adjoint operator in Hilbert space has recently been pointed out by Walter in [36], and his operator-theoretic formulation is adopted here. The use of the eigenfunction expansion is illustrated by applying it to solve a heat-conduction problem for a solid in contact with a fluid.

(Received February 02 1976)