Variational inequalities: an elementary approach (Q2574758)

Let \(M=(m_{ij})\) be an \(n \times n\) matrix with real entries such that \(m_{ij}+m_{ji} \geq 0\), \(i,j=1, \dots, n\). The author proves that the system of inequalities \(x \in {\mathbb R}^n\), \(x \geq 0\), \(Mx \geq 0\) has non--trivial solutions. Applications of the result to the theory of monotone variational inequalities are discussed.