Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T01:21:17.368Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)