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A nonlocal Sturm–Liouville eigenvalue problem

Published online by Cambridge University Press:  14 November 2011

Pedro Freitas
Pedro Freitas
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, U.K.
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Abstract

A nonlocal eigenvalue problem of the form u″ + a(x)u + Bu = λu with homogeneous Dirichlet boundary conditions is considered, where B is a rank-one bounded linear operator and x belongs to some bounded interval on the real line. The behaviour of the eigenvalues is studied using methods of linear perturbation theory. In particular, some results are given which ensure that the spectrum remains real. A Sturm-type comparison result is obtained. Finally, these results are applied to the study of some nonlocal reaction–diffusion equations.

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Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 1 , 1994 , pp. 169 - 188
Copyright
Copyright © Royal Society of Edinburgh 1994

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