A class of nonlinear complementarity problems for multifunctions

Given a continuous mapF:R n →R n and a lower semicontinuous positively homogeneous convex functionh:R n →R, the nonlinear complementarity problem considered here is to findxeR + n andy∈∂h(x), the subdifferential ofh atx, such thatF(x)+y≥0 andx T (F(x)+y)=0. Some existence theorems for the above problem are given under certain conditions on the mapF. An application to quasidifferentiable convex programming is also shown.