例外簇和变分不等式解的存在性

Exceptional Family and the Existence of a Solution to Variational Inequality

为研究变分不等式解的存在性问题 ,本文提出了一个新的例外簇概念 ,并且证明了变分不等式或者有解 ,或者对任意 ^x ,有关于 ^x的一个例外簇 .借助于例外簇的这条性质 ,本文通过证明了变分不等式没有关于 ^x的一个例外簇 ,来说明变分不等式有解 ,从而得出一个变分不等式解的存在性定理 .

This paper proposes a new definition of exceptional family for variational inequality for the study of the existence problem of variational inequality, and has proved that the variational inequality has at least one solution, or there exists an exceptional family with respect to . By means of the proposition of exceptional family, we have proved that the variational inequality has no solution, so the variational inequality has at least one solution. This paper provides an existence theorem for the variational inequality.