In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external potentials satisfy a growth condition near the common points. We then specialize the setting to a specific problem on the real line which arises in the study of c...

This paper introduces the notion of a weighted Complementarity Problem (wCP), which consists in finding a pair of vectors (x, s) belonging to the intersection of a manifold with a cone, such that their product in a certain algebra, x ◦ s, equals a given weight vector w. When w is the zero vector, then wCP reduces to a Complementarity Problem (CP). The motivation for introducing the more general...

we study the equilibrium states for an energy functional with a parametric force field on a region of a surface. consideration of free equilibrium states is based on lyusternik - schnirelman's and skrypnik's variational methods. consideration of equilibrium states under a constraint of geometrical character is based on an analog of skrypnik's method, described in cite{vyr3}. in local coordinate...

In many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. This paper defines a new inverse problem, called “inverse feasible problem”. For a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

The present work considers the following computational problem: Given any finite game in normal form G and the corresponding infinitely repeated game G∞, determine in polynomial time (wrt the representation of G) a profile of strategies for the players in G∞ that is an equilibrium point wrt the limit-of-means payoff. The problem has been solved for two players [10], based mainly on the implemen...

We give an explicit construction of families of Dm-equivariant polynomial vector fields in R possessing a codimension-one homoclinic cycle. The homoclinic cycle consist of m homoclinic trajectories all connected to the equilibrium at the origin. The constructed vector fields can provide a setting for a (numerical) bifurcation study of these homoclinic cycles, in particular for m a multiple of f...

In this paper, we introduce a class of generalized vector equilibrium problems for set-valued mappings which include a number of vector equilibrium problems, generalized vector variational-like inequality problems and generalized vector variational inequality problems as special cases. By using the KKM-Fan theorem and Nadler’s lemma, we prove the existence of solution to this class of generaliz...