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.

在这篇论文中，深受 Aussel 和 Hadjisavvas [关于拟单调变分不等式的启发。J Optim 理论应用程序。2004;121:445–450] 和 Daniilidis 和 Hadjisavvas [非光滑半严格拟凸函数和严格拟凸函数的表征。J Optim 理论应用程序。1999;102(3):525–536]，我们研究了 Hadamard 流形上准单调集值向量场的 Stampacchia 变分不等式解的存在性。此外，存在性结果是在准单调性和上符号连续性等弱假设下获得的。还给出了我们的结果的应用。