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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 K be a closed convex set in a real reflexive Banach space V with dual space V * . For given fV, find uK such that

φ(u,ν)f,ν-u,forallνK,(1)

where φ:K×K 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 φ. Applications to distributed market equilibria with bound and obstacle p-harmonic boundary value problems are given.

MSC:
49J40Variational methods including variational inequalities
74A55Theories of friction (tribology)
74M15Contact (solid mechanics)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)