T-дифференцируемые функционалы и их критические точки

Abstract

The critical points of the functionals F:D ⊂ X → R defined on "nonlinear" sets D in the topological vector spaces X are studied. A construction of a T-derivative is suggested for these functionals and compared with to known constructions. The concept of a weak critical point is introduced and Coleman's principle is justified for T-differentiable functionals.