In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

We consider the probability measure minimizing a free energy functional equal to sum of Coulomb interaction, confinement potential and an entropy term, which arises in statistical mechanics gases. In limit where inverse temperature $\beta$ tends $\infty$ term disappears measure, we call thermal equilibrium well-known can also be interpreted as solution classical obstacle problem. provide quanti...