带有拟单调函数的不等式解的存在性(英文)  

Existence of Solutions of Inequalities Involving Quasimonotone Functions^1

作　　者：侯吉成[1] 

机构地区：[1]烟台大学数学与信息科学系,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2005年第1期1-6,共6页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(10171043;10251002).

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.

关 键 词：不等式 单调性 凸空间 

分 类 号：O177[理学—数学]