We study a system of singular differential equations which arises in a physical model describing the oscillations of a plasma in an equilibrium configuration in a cylindrical domain. The main result is a description of the essential spectrum of this problem as the spectrum of certain multiplication operators. It turns out that in contrast with the so-called hard core problem (where the differential equations are not singular) new intervals of essential spectrum may appear which can be expressed in terms of the asymptotic Hain–Lüst operator. A main tool here is a lemma about the essential spectrum of certain pseudo-differential operators. We also discuss the location of the various parts of the essential spectrum and the question of stability.
(Joint work with R. Mennicken, S. Naboko)