AbstractUsing some imbedding theorems, the Langenbach variational theorem for operator equationPu=f* is obtained as a natural consequence of the Kerner‐Vainberg potentiality theorem coupled with standard results of the variational calculus; in our approach operatorPis defined not over all the spaceXbut only on a dense subspace (compare with [1], pp. 33–34, propositions 3.2 and 3