Variational inequalities and the principle of virtual displacements

The existence of a solution of the inclusion $0\in A(x)+N_Q(x)$ is proved, in which $A$ is a multivalued pseudomonotone operator from the reflexive space $V$ to the conjugate space to it $V^*$, $N_Q$ is a normal cone to the weakly compact and, generally speaking, not convex set $Q \subset V$, with nonzero euler characterization $\chi(Q)$.