The author generates the Babuška-Brezzi theory to a class of nonlinear variational problems with constraints. He considers the operator equations with a dual-dual type structure,
where is given, the operator itself presents also the dual structure , and are linear and bounded, and is nonlinear. He provides sufficient conditions for the existence and uniqueness of solutions to the continuous and Galerkin formulations and derives a Strang-type estimate for the associated error. Moreover, he presents an application to the coupling of mixed finite elements and boundary elements for a nonlinear transmission problem in potential theory.