Title: On the Bogolubov-de Gennes Equations,
Abstract: We consider the Bogolubov-de Gennes equations giving an equivalent
formulation of the BCS theory of superconductivity. We are interested in the
case when the magnetic field is present. We (a) discuss their general features,
(b) isolate key physical classes of solutions (normal, vortex and vortex
lattice states) and (c) prove existence of the normal, vortex and vortex
lattice states and stability/instability of the normal states for large/small
temperature or/and magnetic fields.