Yao, Jen-Chih; Guo, Jong-Shenq Variational and generalized variational inequalities with discontinuous mappings. (English) Zbl 0809.49005 J. Math. Anal. Appl. 182, No. 2, 371-392 (1994). The authors discuss the variational problem: given \(f: X\subset{\mathcal R}^ n\to {\mathcal R}^ n\), to find \(x\in X\) such that \[ \langle f(x), u- x\rangle\geq 0,\qquad\text{for all}\quad u\in X\tag{P}\(_ 1\) \] and its multivalued version: given a multivalued function \(F: X\to 2^{{\mathcal R}^ n}\), to find \(x\in X\), \(y\in F(x)\) such that \[ \langle y,u- x\rangle\geq 0,\qquad\text{for all}\quad u\in X.\tag{P}\(_ 2\) \] More precisely, they consider functions \(f\) and \(F\) which are not necessarily continuous. Several existence results are proved. Furthermore, they provide uniqueness results for problem \((\text{P}_ 2)\) and the complementary one: given a closed convex cone \(K\subset {\mathcal R}^ n\) to find \(x\in K\), \(y\in F(x)\) such that \(y\in K^*\), \(\langle y,x\rangle= 0\), where \(K^*\) denotes the polar cone.Applications to minimization problems for pseudo-convex functions are also investigated. Reviewer: A.Salvadori (Perugia) Cited in 3 ReviewsCited in 29 Documents MSC: 49J40 Variational inequalities Keywords:variational inequalities; pseudo-convex functions PDFBibTeX XMLCite \textit{J.-C. Yao} and \textit{J.-S. Guo}, J. Math. Anal. Appl. 182, No. 2, 371--392 (1994; Zbl 0809.49005) Full Text: DOI