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

George Isac, M. Gabriela Cojocaru



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).


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

Full Text:



  • There are currently no refbacks.

Partnerzy platformy czasopism