  Solutions of some partial differential equations are obtained as critical
points of a real funtional. Then the Banach space where this functional is
defined has to be real, otherwise, it is not differentiable. It follows that
the equation is solved with respect to the real dual space of this Banach
space. But if the solution is complex-valued there is the following problem:
what does the multiplication of this equation by a complex number mean ? In
this note, we explain how to rigorously define this operation.
