Non-zero solutions for a class of generalized variational inequalities in reflexive Banach spaces

Abstract

In this paper, we study the existence of nonzero solutions for a class of generalized variational inequalities involving setcontractive mappings by using the fixed point index approach in reflexive Banach spaces. Under some suitable assumptions, we show some new existence theorems of nonzero solutions for this class of generalized variational inequalities in reflexive Banach spaces.

Nonzero Solutions of Generalized Variational Inequalities

“…by [2,3], where According to Brouwer's fixed point theorem (see [2,3]), there exists m m u K ∈ satisfying the equality (9), that is, m u is a solution of the variational inequality (6).…”

“…[8] discussed the variational inequality (1) when A is coercive or monotone and g is set-contractive or upper semi-continuous. [9] considered the variational inequality (1) when A is single-valued continuous and g is set-contractive.…”

The Nonzero Solutions and Multiple Solutions for a Class of Bilinear Variational Inequalities

“…Recently, several authors discussed the existence of nonzero solutions for variational inequalities in Hilbert or Banach spaces (see [4] and the references therein).…”