Sobre princípios minimax para uma classe de funcionais semicontínuos inferiormente.

Abstract

Recent studies on the Critical Point Theory has as main goal the development of variacional methods for functionals that are not of C1 class. These studies have implicitly the generalization of the notion of critical point as being a point u ∈ X, such that I′(u) = 0, with X a Banach space and I ∈ C1(X,R) (see [8], [7] and [25]). Our work is devoted to study the generalized critical point theory which was proposed by Szulkin in [25]. We present the definition of generalized critical point for a class of functional I : X −→ (−∞,∞], with I = Φ + Ψ, Φ ∈ C1(X,R) and Ψ : X −→ (−∞,∞] is a convex, proper (do not occur Ψ ≡ ∞) and is a lower semicontinuous functional; we also study some minmax type results for those functionals and we finish with aplications of these results.