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.
出处
《系统科学与数学》
CSCD
北大核心
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
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
Local convex space, set-valued mapping, extreme minimum fixed point theorem, ill-posed operator equation.
