Fréchet空间上集值微分方程初值问题的收敛性  

Convergence of initial value problem for set differential equations in Fréchet space

作　　者：王培光[1] 邢珍钰 WANG Peiguang;XING Zhenyu(College of Mathematics and Information Science,Hebei University,Baoding 071002,China)

机构地区：[1]河北大学数学与信息科学学院,保定071002

出　　处：《黑龙江大学自然科学学报》2018年第5期516-523,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11771115; 11271106)

摘　　要：研究一类Fréchet空间F上的集值微分方程初值问题,基于对Fréchet空间上所有紧致凸子集构成的空间K_c(F)可视为半线性度量空间K_c(E^i)的投影极限的研究,引入K_c(F)中Hukuhara导数的定义。利用拟线性化方法和比较原理,构造单调迭代序列,证明在K_c(F)空间上,集值微分方程初值问题的逼近解序列一致且平方收敛于方程的唯一解。A class of initial value problems for set differential equations in Fréchet space is investigated.Based on the set K_c(F) of all compact convex subsets of a Fréchet space F,which is considered as a projective limit of semilinear metric space K_c(Ei),the definition of Hukuhara derivative is introduced. By using the method of quasilinearization and comparison principle,two monotone iterative sequences in K_c(F) are constructed,and it shows that the sequences of approximate solutions converge uniformly and quadratically to the unique solution of the problem.

关 键 词：FRÉCHET空间 集值微分方程 拟线性化方法 一致收敛 平方收敛 

分 类 号：O175.12[理学—数学]