VARIATIONAL INEQUALITIES: AN ELEMENTARY APPROACH

Claudio BAIOCCHI Dipartimento di Matematica – Università di Roma “La Sapienza” P.le Aldo Moro 2 – 00185 Roma, Italy

                     baiocchi@mat.uniroma1.it

Abstract. We will deal with the following problem:

Let M be an n × n matrix with real entries. Under which conditions the family of inequalities:

x ≥ 0; M · x ≥ 0

has non–trivial solutions x ∈ R^{n}?

A simple sufficient condition will provide a general existence theorem for Variational Inequalities in the framework of monotone operators.