On a class of saddle point problems and convergence results - Chivu Cojocaru, Mariana; Matei, Andaluzia (Mathematical Modelling and Analysis, 2020)
We consider an abstract mixed variational problem consisting of two inequalities. The ﬁrst one is governed by a functional φ, possibly non-diﬀerentiable. The second inequality is governed by a nonlinear term depending on a non negative parameter ǫ. We study the existence and the uniqueness of the solution by means of the saddle point theory. In addition to existence and uniqueness results, we deliver convergence results for ǫ → 0. Finally, we illustrate the abstract results by means of two examples arising from contact mechanics.