带有拟单调函数的不等式解的存在性

摘要

大量的非线性边界值问题可以借助单调算子理论来处理.这个理论的两个基本结果是Debrunner-Flor的单调延拓定理和关于变分不等式的Hartman-Stampacchia定理.在1983年Lassonde拓广这两个定理到凸空间,并且通过减弱空间的紧性改进了这两个定理.本文在凸空间结构中通过减弱函数的单调性建立了某些新的Lassonde型的不等式解的存在性定理.%A large amount of nonlinear boundary value problems may be treated with the help of the theory of monotone operators. Two of the basic results of this theory are the Debrunner-Flor monotone extention theorem and the Hartman-Stampacchia theorem on variational inequalities. In 1983, Lassonde extended and improved the Debrunner and Flor's theorem and Hartman and Stampacchia's theorem in a convex space under a relaxation of the compactness assumption.It is our object in this paper to establish Lassonde type theorems under an assumption greatly weaker than semimonotonicity.