Principal Eigenvalues for Generalised Indefinite Robin Problems

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 and Warma (Potential Anal 19:341–363, 2003). Examples of simple domains with cusps are used to illustrate all possible phenomena.