  We connect the well-known theory of functional forms of variational bicomplex
with the theory of antiexact differential forms. We identify antiexact
functional forms as an obstruction to the variationality of differential
equations. The most prominent result of this observation is the formulation of
the variational problem for some differential equations that are not
variational and neither have a variational multiplier. Heat, Navier-Stokes, and
KdV equations illustrate this new variational principle.
