中文摘要：

考虑一类偏微分包含边值问题：-△u∈extG（x，u）．当集值函数G（x，u）为有界紧凸值的、关于变量x是可测的、关于变量u是连续的时，利用Tolstonogov端点连续选择定理，证明了其端点解的存在性．

英文摘要：

This paper deals with the boundary value problems for a class of partial differential inclusions -△u∈extG（x,u） takes bounded, weakly compact, convex values, and is measurable about variable x, is continuous about variable u, we proved the existence of extremal solutions on the basis of Tolstonogov extremal continuous selection theorem.