Critical points of non-smooth functions with a weak compactness condition

Weak∗ Smooth Compactness in Smooth Topological Spaces

In this paper we obtain some properties of the weak smooth α-closure and weak smooth α-interior of a fuzzy set in smooth topological spaces and introduce the concepts of several types of weak∗ smooth compactness in smooth topological spaces and investigate some of their properties.

Critical points of simple functions

A non-smooth three critical points theorem with applications in differential inclusions

We extend a recent result of Ricceri concerning the existence of three critical points of certain non-smooth functionals. Two applications are given, both in the theory of differential inclusions; the first one concerns a non-homogeneous Neumann boundary value problem, the second one treats a quasilinear elliptic inclusion problem in the whole RN .

A Weak Grothendieck Compactness Principle

The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in...

Approximation by Smooth Functions with No Critical Points on Separable Banach Spaces

We characterize the class of separable Banach spaces X such that for every continuous function f : X → R and for every continuous function ε : X → (0,+∞) there exists a C smooth function g : X → R for which |f(x)− g(x)| ≤ ε(x) and g′(x) 6= 0 for all x ∈ X (that is, g has no critical points), as those infinite dimensional Banach spaces X with separable dual X∗. We also state sufficient condition...