On a class of saddle point problems and convergence results

• Published in: Mathematical modelling and analysis Vol. 25; no. 4; pp. 608 - 621
• Main Authors: Chivu Cojocaru, Mariana, Matei, Andaluzia
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 13.10.2020
• Subjects: Convergence; Convergence (Mathematics); convergence result; Estimates; Hypotheses; Inequalities (Mathematics); Mathematical research; Mechanics; mixed variational problem; penalty term; saddle point; Saddle points; Uniqueness; Romania; saddle point; mixed variational problem; convergence result; penalty term
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/mma.2020.11140

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.