Uniqueness of the principal eigenvalue in nonlocal boundary value problems

Webb, J.R.L. (2008) Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems: Series S, 1(1), pp. 177-186. (doi: 10.3934/dcdss.2008.1.177)

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Abstract

In the study of nonlinear boundary value problems, existence of a positive solution can be shown if the nonlinearity 'crosses' the principal eigenvalue, the eigenvalue corresponding to a positive eigenfunction. It is well known that such an eigenvalue is unique for symmetric problems but it was unclear for general nonlocal boundary conditions. Here some old results due to Krasnosel'skiĭ are applied to show that the nonlocal problems which have been well studied over the last few years do have a unique principal eigenvalue. Some estimates and some comparison results are also given.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Webb, Professor Jeffrey
Authors: Webb, J.R.L.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Discrete and Continuous Dynamical Systems: Series S
ISSN:1937-1632
ISSN (Online):1937-1179
Published Online:01 December 2007

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