BLOWING-UP PROPERTIES OF THE POSITIVE PRINCIPAL EIGENVALUE FOR INDEFINITE ROBIN-TYPE BOUNDARY CONDITIONS

摘要

In this paper, we consider the positive principal eigenvalue for some linear elliptic eigenvalue problem with Robin-type boundary conditions having indefinite coefficients, where its asymptotic behavior for indefinite varying weights is investigated. The aim of this paper is to study necessary and sufficient conditions for the positive principal eigenvalue to blow up to infinity. The analysis is based on variational characterization of the positive principal eigenvalue.