Sur un théorème variationnel de Langenbach

Using some imbedding theorems, the Langenbach variational theorem for operator equation Pu=f* is obtained as a natural consequence of the Kerner-Vainberg potentiality theorem coupled with standard results of the variational calculus; in our approach operator P is defined not over all the space X but only on a dense subspace (compare with 1], pp. 33–34, propositions 3.2 and 3.3).