Existence conditions in variational inclusions with constraints

Abstract

In this article we study a general variational inclusion problem with constraints. An existence theorem is given for the scalar problem which allows us to derive several results on existence of solutions of variational inequality and variational inclusion models in which the set-valued data are present.

Keywords:

• Variational inclusion
• Properly quasimonotone map
• Equilibrium problem
• Mathematics Subject Classification 2000: 49J53
• 47N10
• 47J20