局部凸空间中集值映射的极小不动点定理及其应用  

MINIMUM FIXED POINT THEOREM FOR SET-VALUED MAPPING IN THE LOCAL CONVEX SPACE AND ITS APPLICATION

作　　者：徐明跃[1] 曹玉红[1] 王玉文[1] 

机构地区：[1]哈尔滨师范大学数学系,黑龙江150080

出　　处：《系统科学与数学》2007年第6期943-952,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10671049);黑龙江省自然科学基金(A02004-09);黑龙江省教育厅科学技术项目(10553024)资助

摘　　要：利用局部凸空间中Fan-Kakutani不动点定理,得到局部凸空间中集值映射的极小不动点定理,应用此定理,证明了半线性不适定的算子方程的最小范数极值解的存在性.此结果可以应用到不适定常微方程的两点边值问题,不适定偏微方程的边值问题.In this paper, by Fan-Kakutani fixed point theorem,it is obtained that the minimum fixed point theorem for set-valued mapping in the local convex space. Applying this theorem, the existence of the minimal norm extrimal solution to semilinear ill-posed operator equation is proved. The results can be applied to the ill-posed two-points boundary problem for differential equation.

关 键 词：局部凸空间 集值映射 极小不动点定理 不适定算子方程 

分 类 号：O189[理学—数学]