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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (1): 71-84.doi: 10.3969/j.issn.1005-3085.2019.01.006

• • 上一篇    下一篇

半线性时滞模糊微分方程解的存在性

刘   娟,   肖建中,   姚忠豪   

  1. 南京信息工程大学数学与统计学院，南京  210044
  • 收稿日期:2016-10-21 接受日期:2017-05-08 出版日期:2019-02-15 发布日期:2019-04-15

Existence of Solutions for Semilinear Delay Fuzzy Differential Equations

LIU Juan,   XIAO Jian-zhong,   YAO Zhong-hao   

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044
  • Received:2016-10-21 Accepted:2017-05-08 Online:2019-02-15 Published:2019-04-15

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摘要： 模糊微分方程常用来模拟不确定条件下的变化过程．其理论被广泛的应用在很多不同的实际问题上．本文主要研究半线性时滞模糊微分方程解的存在性．在广义Hukuhara导数的框架下，运用了一个弱压缩映射的不动点定理，将半线性时滞模糊微分方程解的存在性问题转化为算子不动点的存在性问题，从而建立了方程解的存在性定理．文中例子说明了该理论结果的实用性．

关键词: 弱压缩映射, 时滞微分方程, 模糊微分方程

Abstract: Fuzzy differential equations are commonly used to describe the changing process with uncertain conditions. And its theory is widely applied to many different practical problems. The aim of this paper is to study the existence of solutions for semilinear delay fuzzy differential equations. We use a fixed point theorem of weakly contractive mappings to transform the existence of solutions into the existence of fixed points of an operator, and establish the theorem of existence of solutions for the equations. In addition, an example is given to illustrate the applicability of the theoretical results.

Key words: weakly contractive mappings, delay differential equations, fuzzy differential equations

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