On quasimonotone Stampacchia variational inequalities on Hadamard manifolds

In this paper, which is deeply inspired from Aussel and Hadjisavvas [On quasimonotone variational inequalities. J Optim Theory Appl. 2004;121:445-450] and Daniilidis and Hadjisavvas [Characterization of nonsmooth semistrictly quasiconvex and strictly quasiconvex functions. J Optim Theory Appl. 1999;102(3):525-536], we study the existence of solutions of the Stampacchia variational inequality for a quasimonotone set-valued vector field on a Hadamard manifold. Moreover, the existence results are obtained under weak assumptions like quasimonotonicity and upper-sign continuity. An application of our results is also given.