  Following Bogomolnyi's classical treatment of vortices, we develop a method
for finding rigorous lower bounds to the Landau-Ginzburg free energy describing
unconventional superconductors in the absence of external magnetic fields. This
allows a more precise description of the magnetic instabilities previously
considered in these systems. In particular, we derive new sufficient conditions
for the stability of both the homogeneous and inhomogeneous equilibrium states.
