一类广义混合变分不等式及其在电子线路中的应用

The generalized mixed variational inequality is an important extension of the classical variational inequality. There are extensive application.backgrounds in economic equilibriums, network energy controls, electronic circuits and other fields in science and engineering. This project.is devoted to study the existence and stability of solutions for a class of generalized mixed variational inequalities and apply the existence .and stability results to the stability of currents in electronic circuits. Based on the previous research work, by using topological degree methods, combinating with the theories, methods and skills of nonlinear monotone operators, set value analysis et. al, we establish the degree theory for a class of generalized mixed variational inequalities with S+ multimaps and pseudo-monotone multimaps, obtain the stability and existence of solutions for the class of generalized mixed variational inequalities and apply the above research results obtained to study the stability of currents in a class of electronic circuits. The research of these problems can enrich and develop the theories, methods and skills of the variational inequality, and have important scientific significances. Moreover, the research results of them can be applied to deal some practical problems from the economic equilibriums, the network energy controls and the electronic circuits and other fields of science and engineering, and have important application values.

广义混合变分不等式是经典变分不等式的一种重要推广，在经济均衡，网络能量控制与电子线路等科学和工程领域有着广泛的应用背景。本项目主要研究一类广义混合变分不等式解的存在性和稳定性及其对电子线路中电流稳定性问题的应用。我们将在以往研究工作的基础上，利用拓扑度方法，结合非线性单调算子和集值分析等领域的理论，方法和技巧，建立涉及S+ 集值映射与伪单调集值映射的广义混合变分不等式的度理论，获得该类广义混合变分不等式解的存在性与稳定性，并将相关研究结果应用于一类电子线路中电流稳定性问题。这些问题的研究不仅可以丰富和发展变分不等式的理论，方法与技巧，具有重要的科学意义，而且研究结果可以应用于解决经济均衡，网络能量控制与电子线路等科学和工程领域的一些实际问题，具有重要的应用价值。

广义混合变分不等式是经典变分不等式的一种重要推广，在经济均衡，网络能量控制与电子线路等科学和工程领域有着广泛的应用背景。本项目主要研究一类广义混合变分不等式解的存在性和稳定性及其对电子线路中电流稳定性问题的应用。我们已经研究了一类广义混合变分不等式解的存在性。所得到的结果可用于一些非正则电子线路，如文献（J. Optim. Theory Appl. (2008) 138: 397–406）中所给出的非正则电子线路。