We verify -after appropriate modificationsan old conjecture of Brezis-Ekeland [3] concerning the feasibility of a global and variational approach to the problems of existence and uniqueness of solutions of non-linear transport equations, which do not normally fit in an Euler-Lagrange framework. Our method is based on a concept of “anti-self duality” that seems to be inherent in many problems, i...

This paper has two parts. The mathematical part provides generalized versions of the robust Ekeland variational principle in terms set-valued EVP with variable preferences, uncertain parameters and changing weights given to vectorial perturbation functions. behavioural that motivates our findings models formation stability a partnership changing, complex environment context rationality approach...

A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll they have the same minimal period. In this paper, we provide a characterization of forms for convex spheres Riemannian unit tangent bundles in terms $S^1$-equivariant spectral invariants. Furthermore, restricted type hypersurfaces symplectic Euclidean spaces, give sufficient condition property via Ekeland-Ho...

What happens to the conclusion of the Ekeland variational principle (briefly, EVP) if a considered function f : X → R ∪ {+∞} is lower semicontinuous not on a whole metric space X but only on its domain? We provide a straightforward proof showing that it still holds but only for varying in some interval ]0, β − infX f [, where β is a quantity expressing quantitatively the violation of the lower ...

We study a restricted weak lower semicontinuity property, which we call the (PS)-weak lower semicontinuity, for a smooth integral functional on the Sobolev space along all weakly convergent Palais-Smale sequences of the functional. By the Ekeland variational principle, the (PS)-weak lower semicontinuity is sufficient for the existence of minimizers under the usual coercivity assumption. In gene...

In this paper, we present a few recent existence results via variational approach for the Cauchy problem dy dt (t) + A(t)y(t) ∋ f(t), y(0) = y0, t ∈ [0, T ], where A(t) : V → V ′ is a nonlinear maximal monotone operator of subgradient type in a dual pair (V, V ′) of reflexive Banach spaces. In this case, the above Cauchy problem reduces to a convex optimization problem via Brezis–Ekeland device...

The classical Pfaff-Darboux Theorem, which provides local ‘normal forms’ for 1-forms on manifolds, has applications in the theory of certain economic models [3]. However, the normal forms needed in these models come with an additional requirement of convexity, which is not provided by the classical proofs of the Pfaff-Darboux Theorem. (The appropriate notion of ‘convexity’ is a feature of the e...