Principal eigenvalues for generalised indefinite Robin problems

Abstract

We consider the principal eigenvalue of generalised Robin boundary value problems on non-smooth domains, where the zero order coefficient of the boundary operator is negative or changes sign. We provide conditions so that the related eigenvalue problem has a principal eigenvalue. We work with the framework involving measure data on the boundary due to [Arendt & Warma, Potential Anal. 19, 2003, 229-231]. Examples of simple domains with cusps are used to illustrate all phenomena occurring.