  This article develops optimality conditions for a large class of non-smooth
variational models. The main results are based on standard tools of functional
analysis and calculus of variations. Firstly we address a model with equality
constraints and, in a second step, a more general model with equality and
inequality constraints, always in a general Banach space context. We highlight
the results in general are well known, however, some novelties are introduced
related to the proof procedures, which are in general softer than those
concerning the present literature.
