【摘要】 研究有限维空间中的联立变分不等式问题.给出该问题的一般提法及应用背景,通过将该问题中的每一项都视为含参数的变分不等式,从而可以确定以参数为自变量、关于其解的隐函数,并在函数严格单调的假设下,证明了此隐函数的连续性.基于此,利用Brouwer不动点定理,得到了原问题的解的存在性,并在可行域为箱形且整体变分函数严格单调情形下证明了解的唯一性,当可行域非箱形时,所举反例表明解可以是不唯一的.更多还原

【Abstract】 A system of variational inequalities (SVI) is proposed and investigated.An application of the SVI to the three-dimensional frictional contact problem is presented.When the functions defining the SVI are strictly monotone,an existence theorem of the SVI is proved by studying the continuity of implicit functions determined by the parametric variational inequalities in the SVI and using Brouwer′s fixed point theorem.Furthermore,the uniqueness of the solution is proved under the conditions that the whole function defining the SVI is strictly monotone and the feasible region is a box.Some counter examples with infinite solutions can be easily found when the feasible region is not a box.更多还原