Functions without exceptional family of elements and the solvability of variational inequalities on unbounded sets

George Isac, M. Gabriela Cojocaru

DOI: http://dx.doi.org/10.12775/TMNA.2002.041

Abstract


In this paper we prove an alternative existence theorem for
variational inequalities defined on an unbounded set in a Hilbert space.
This theorem is based on the concept of exceptional family of elements
(EFE) for a mapping and on the concept of $(0, k)$-epi mapping which is
similar to the topological degree. We show that when a k-set field is without
(EFE) then the variational inequality has a solution. Based on this result
we present several classes of mappings without (EFE).

Keywords


Variational inequalities; (0; k)-epi mappings and exceptional family of elements for a mapping

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