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.


49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J53 Set-valued and variational analysis
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