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Blowing-up of principal eigenvalues for Neumann boundary conditions

Published online by Cambridge University Press:  27 June 2008

Kenichiro Umezu
Kenichiro Umezu
Affiliation:
Faculty of Engineering, Maebashi Institute of Technology, Maebashi 371-0816, Japan ([email protected])
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Abstract

This paper studies blowing-up properties of a unique positive principal eigenvalue for a linear elliptic eigenvalue problem with an indefinite weight function and Neumann boundary condition. Necessary and sufficient conditions for the blowing-up property are discussed, based on the variational characterization of the unique positive principal eigenvalue. A counterexample is constructed, which shows that a known necessary and sufficient condition for the blowing-up property in the Dirichlet boundary condition case no longer remains true in the Neumann case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 3 , June 2007 , pp. 567 - 579
Copyright
2007 Royal Society of Edinburgh

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