Two stability problems related to resistive magnetohydrodynamics

Two general problems related to resistive magnetohydrodynamic stability are addressed in this paper. First, a general stability condition previously derived by the author for a class of real systems, occurring especially in plasma physics, is proved to persist to second order, despite the addition of several antisymmetric operators of first order in the linearized stability equation. Second, for a special but representative choice of the stability operators, a nonperturbative analysis demonstrates the existence of a critical density for the appearance of an overstability and the connected Hopf bifurcation, as suggested in a previous paper [Phys. Lett. A 180, 257 (1993)]