Fréchet空间上集值微分方程初值问题解的高阶收敛性 王培光, 邢珍钰, 吴曦冉河北大学数学与信息科学学院 保定 071002 Higher-Order Convergence of Solutions of Initial Value Problem for Set Differential Equations in Fréchet Space Pei Guang WANG, Zhen Yu XING, Xi Ran WUCollege of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China

摘要 图/表 参考文献 相关文章 全文: PDF(523 KB) HTML (1 KB) 输出: BibTeX | EndNote (RIS) 摘要本文讨论一类Fréchet空间F上的非线性集值微分方程初值问题解的收敛性.基于Fréchet空间F上所有紧致凸子集构成的空间Kc（F）可视为半线性度量空间Kc（Ei）的投影极限和投影极限的性质，通过引入集值函数的Fréchet偏导数以及集值函数的超凸和超凹性定义，应用比较原理和拟线性方法，对所构造的单调迭代序列进行分析，得到了在Kc（F）空间上集值微分方程初值问题的迭代解序列一致且高阶收敛于方程唯一解的判别准则.所得结果发展了Fréchet空间上的微分方程理论. 服务 加入引用管理器 E-mail Alert RSS 收稿日期: 2020-01-20 MR (2010): O175.12 O177.92 基金资助:国家自然科学基金资助项目（11771115，11271106） 作者简介: 王培光,E-mail:pgwang@hbu.edu.cn;邢珍钰,E-mail:smaths2@hbu.edu.cn;吴曦冉,E-mail:xrwu2017@163.com 引用本文: 王培光, 邢珍钰, 吴曦冉. Fréchet空间上集值微分方程初值问题解的高阶收敛性[J]. 数学学报, 2021, 64(3): 427-442. Pei Guang WANG, Zhen Yu XING, Xi Ran WU. Higher-Order Convergence of Solutions of Initial Value Problem for Set Differential Equations in Fréchet Space. Acta Mathematica Sinica, Chinese Series, 2021, 64(3): 427-442. 链接本文: http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2021/V64/I3/427 [1] Abbas U., Lupulescu V., Set functional differential equations, Commun. Appl. 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