Gelʹfandʹs equation in spherical domains: II. Further results and the spherical annulus revisited

Gelʹfandʹs equation in a sphere is revisited. In a spherical annulus, it is proved to have the properties of finite multiplicity (for the annulus) suggested by earlier computations. In this paper, further analysis is provided which suggests that the gross multiplicity in three (or more—up to ten) dimensions is a property of simply-connected domains only. The case of a “hot core” and finite Biot number on the outside of the spherical annulus is amenable to the same analysis.