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Zbl 1130.49302
Bianchi, M.; Hadjisavvas, N.; Schaible, S.
Minimal coercivity conditions and exceptional families of elements in quasimonotone variational inequalities. (English)
[J] J. Optim. Theory Appl. 122, No. 1, 1-17 (2004). ISSN 0022-3239; ISSN 1573-2878/e

Summary: A coercivity condition is usually assumed in variational inequalities over noncompact domains to guarantee the existence of a solution. We derive minimal, i.e., necessary coercivity conditions for pseudomonotone and quasimonotone variational inequalities to have a nonempty, possibly unbounded solution set. Similarly, a minimal coercivity condition is derived for quasimonotone variational inequalities to have a nonempty, bounded solution set, thereby complementing recent studies for the pseudomonotone case. Finally, for quasimonotone complementarity problems, previous existence results involving so-called exceptional families of elements are strengthened by considerably weakening assumptions in the literature.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators

Keywords: variational inequalities; quasimonotone maps; pseudomonotone maps; coercivity conditions; exceptional families of elements

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