  We consider equations of the form Bf=g, where B is a Galois connection
between lattices of functions. This includes the case where B is the
Legendre-Fenchel transform, or more generally a Moreau conjugacy. We
characterise the existence and uniqueness of a solution f in terms of
generalised subdifferentials. This extends a theorem of Vorobyev and
Zimmermann, relating solutions of max-plus linear equations and set coverings.
We give various illustrations.
