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On quasimonotone variational inequalities. (English) Zbl 1062.49006
Summary: The purpose of this paper is to prove the existence of solutions of the Stampacchia variational inequality for a quasimonotone multivalued operator without any assumption on the existence of inner points. Moreover, the operator is not supposed to be bounded valued. The result strengthens a variety of other results in the literature.

MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
49J53Set-valued and variational analysis