Blowing-up of principal eigenvalues for Neumann boundary conditions
Kenichiro Umezu · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2007
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.