Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis

Abstract

This paper is concerned with the study of the solution existence of variational inequalities and generalized variational inequalities in reflexive Banach spaces with pseudomonotone operators in the sense of Brezis. The obtained results cover some preceding results in Browder (J. Funct. Anal. 11:251---294, 1972), Brezis (Ann. Inst. Fourier 18:115---175, 1968), Kinderlehrer and Stampacchia (An Introduction to Variational Inequalities and Their Applications, Academic Press, San Diego, 1980), Zeidler (Nonlinear Functional Analysis and Its Applications, II/B, Springer, Berlin, 1990).