Stability of monotone variational inequalities with various applications. (English) Zbl 0848.49006
Giannessi, F. (ed.) et al., Variational inequalities and network equilibrium problems. Proceedings of a conference, Erice, Italy, June 19-25, 1994. New York, NY: Plenum, 123-142 (1995).
Let be a closed convex set in a real reflexive Banach space with dual space . For given , find such that
where satisfies the appropriate convexity and monotonicity assumptions. This problem was introduced by E. Blum and W. Oettli [Math. Stud. 63, No. 1-4, 123-145 (1994)]. In this paper, the convergence and stability theory for variational inequality (1) is studied using the technique of Mosco and the montonicity of . Applications to distributed market equilibria with bound and obstacle -harmonic boundary value problems are given.
|49J40||Variational methods including variational inequalities|
|74A55||Theories of friction (tribology)|
|74M15||Contact (solid mechanics)|
|90C33||Complementarity and equilibrium problems; variational inequalities (finite dimensions)|