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Perturbation of two-point boundary value problems with eigenvalue parameter in the boundary conditions

Published online by Cambridge University Press:  14 November 2011

Lawrence Turyn
Lawrence Turyn
Affiliation:
Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435, U.S.A
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Synopsis

We discuss smooth changes of eigenvalues under perturbation of the boundary value problems given in the title. The simple eigenvalue criterion is developed in the setting of Banach spaces, so very general perturbations of both the differential equation and the boundary conditions are allowed. Further, we need no assumptions about self-adjointness of the original or perturbed problems. The discussion is concluded with the application of the simple eigenvalue criterion to two examples.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 3-4 , 1983 , pp. 213 - 219
Copyright
Copyright © Royal Society of Edinburgh 1983

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