Solvability of a mixed variational problem

Abstract

We consider a variational problem arising from contact mechanics, that consists into a system of two variational inequalities involving Lagrange multipliers. Using elements of convex analysis, we prove the existence of at least one solution. Moreover, the uniqueness and the stability are discussed.

2000 Mathematics Subject Classification. Primary 47N10; Secondary 46T20.

Key words and phrases. saddle point, Lagrange multiplier, mixed variational problem.