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

Published online by Cambridge University Press:  14 February 2012

Charles T. Fulton
Charles T. Fulton
Affiliation:
Department of Mathematics, The Pennsylvania State University
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Synopsis

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 3-4 , 1977 , pp. 293 - 308
Copyright
Copyright © Royal Society of Edinburgh 1977

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