ABSTRACT
The subject of variational inequalities has its origin in the calculus of variation associated with the minimization of infinite dimensional functionals. On the basis of a contact problem studied by Signorini, Fichera [78] carried on a research and proposed the terminology of a variational inequality for the formulation of the Signorini’s contact problem. Stampacchia [197] simultaneously began the study of variational inequalities. In this research, he implicated some scholars, like, Hartman, Lions, etc. [29, 129]. Auslender [22], Bre´zis [38], Browder [40], Hartman and Stampacchia [100], Lions and Stampacchia [148], Minty [161, 162], Rockafellar [181], and Stampacchia [198] obtained several existence results for a solution of variational inequalities with or without using monotonicity condition.
