In this paper we study a class of quasi-variational-hemivariational inequalities in reflexive Banach spaces. The inequalities contain a convex potential, a locally Lipschitz superpotential, and a implicit obstacle set of constraints. Solution existence and compactness of the solution set to the inequality problem are established based on the Kakutani–Ky Fan fixed point theorem. The applicability of the results is illustrated by the steady-state Oseen model of a generalized Newtonian incompressible fluid with mixed boundary conditions. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier-Fujita slip condition, and a generalization of the threshold slip and leak condition of frictional type.

在本文中，我们研究了自反 Banach 空间中的一类准变分半变分不等式。不等式包含一个凸势、一个局部 Lipschitz 超势和一个隐含的障碍约束集。不等式问题的解集的解存在性和紧致性是基于 Kakutani-Ky Fan 不动点定理建立的。具有混合边界条件的广义牛顿不可压缩流体的稳态 Oseen 模型说明了结果的适用性。后者涉及单边边界条件、Navier 滑移条件、非线性 Navier-Fujita 滑移条件的非单调版本，以及摩擦类型的阈值滑移和泄漏条件的推广。