We devise a framework encompassing the classical theory of characteristics and the theory valid in the convex case recently obtained by R.T. Rockafellar and P. Wolenski. It relies on a notion of transform introduced by I. Ekeland. It involves a class of functions called Ekeland functions which is large enough to encompass convex functions, concave functions and linear-quadratic functions, as we...

For subsets in the standard symplectic space $(\mathbb{R}^{2n},\omega_0)$ whose closures are intersecting with coisotropic subspace $\mathbb{R}^{n,k}$ we construct relative versions of Ekeland-Hofer capacities respect to $\mathbb{R}^{n,k}$, establish representation formulas for such bounded convex domains $\mathbb{R}^{n,k}$. We also prove a product formula and fact that value this capacity on h...

We finally understand. Things are the way they are because they can't be otherwise. Ivar Ekeland

In this report we will study the origins and history of functional analysis up until 1918. We begin by studying ordinary and partial differential equations in the 18th and 19th century to see why there was a need to develop the concepts of functions and limits. We will see how a general theory of infinite systems of equations and determinants by Helge von Koch were used in Ivar Fredholm’s 1900 ...

We prove versions of Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces, the equivalence between these principles, as well their to some completeness results for underlying space. These extend proved S.~Cobza\c{s}, Topology Appl. \textbf{265} (2019), 106831, 22, spaces. The key tools are Picard sequences special set-valued mappings on a space $X$, defined terms preorder...

In this note we give a Brøndsted-Rockafellar Theorem for diagonal subdifferential operators in Banach spaces. To this end we apply an Ekeland-type variational principle for monotone bifunctions.

We shall show that a recent version of Ekeland's principle in F-type topological spaces due to Fang from 1996 is implied by the Brezis-Browder principle on ordered sets. We give a series of equivalent formulations of Ekeland's principle in F-type topo-logical spaces, i.e. Penot's ower petal theorem, Takahashi's minimization principle and two theorems due to Oettli and Th era and show the equiva...

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.