In this paper, we deal with the weakly homogeneous generalized variational inequality, which provides a unified setting for several special variational inequalities and complementarity problems studied in recent years. By exploiting weakly homogeneous structures of involved map pairs and using degree theory, we establish a result which demonstrates the connection between weakly homogeneous generalized variational inequalities and weakly homogeneous generalized complementarity problems. Subsequently, we obtain a result on the nonemptiness and compactness of solution sets to weakly homogeneous generalized variational inequalities by utilizing Harker–Pang-type condition, which can lead to a Hartman–Stampacchia-type existence theorem. Last, we give several copositivity results for weakly homogeneous generalized variational inequalities, which can reduce to some existing ones.

在本文中，我们处理了弱齐次广义变分不等式，它为近年来研究的几个特殊的变分不等式和互补性问题提供了统一的设置。通过利用所涉及的映射对的弱齐次结构并使用度数理论，我们建立了一个结果，证明了弱齐次广义变分不等式与弱齐次广义互补问题之间的联系。随后，我们利用Harker-Pang型条件获得了弱集广义变分不等式解集的非空性和紧致性的结果，这可能导致Hartman-Stampacchia型存在定理。最后，对于弱均质的广义变分不等式，我们给出了几个正定性结果，