扰动广义混合变分不等式的可解性

Solvability for Generalized Mixed Variational Inequalities with Perturbation

本文主要研究扰动的广义混合变分不等式解的存在性问题。对集值映射引入2种扰动方式:一种是通过连续的单值映射进行扰动;另一种是通过约束集的闸锥内部的向量进行扰动。在较弱的强制性条件下证明了扰动问题解的存在性。本文的结果在经济领域的某些价格均衡模型中有潜在的应用价值,推广和改善了一些新近文献的相应结果。

The existence of solutions for a generalized mixed variational inequality with perturbation is investigated in this paper. Two perturbed ways of a set valued mapping are introduced： one is perturbed by a continuous and single-valued mapping,and the other is perturbed by a vector in the interior of the barrier cone of the constrained set. Under rather weak conditions, it is shown that the generalized mixed variational inequality perturbed by two ways mentioned above has a solution. The main results may be used in some price equilibrium model in the field of economics, which generalize and improve some known results.