A unified approach for a class of problems involving a pseudo-monotone operator. (English) Zbl 1157.47046

In this paper, the authors consider a variational inequality problem over the union of a set and a sequence of sets, and also over only the union of sets. They obtain an abstract existence result for a solution of such a variational inequality problem and the established a Hartman-Stampacchia type result for the solutions. The study is motivated by the unifying effect of such a result and its large applicability. The authors use their abstract result to prove various existence and approximation results for a class of variational-hemivariational inequalities involving pseudo-monotone operators. Their approach mainly relies on Galerkin like approximations, pseudo-monotone operators and topics from nonsmooth analysis.


47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
49J52 Nonsmooth analysis
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