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非线性微分方程的Hyers-Ulam稳定性
  • ISSN号：1000-9965
  • 期刊名称：《暨南大学学报：自然科学与医学版》
  • 时间：0
  • 分类：O177.2[理学—数学;理学—基础数学]
  • 作者机构：[1]中山大学数学系,广东广州510275, [2]广州松田职业学院,广东广州511370
  • 相关基金：国家自然科学基金资助项目（10871213）
作者： 黎永锦[1], 华柳斌[2]
关键词： HYERS-ULAM稳定性, 非线性微分方程, 边界条件, Hyers-Ulam stability, nonlinear differential equation, initial conditions
中文摘要：

证明了非线性微分方程YY’=1在边界条件Y（n）=1下具有Hyers—Ulam稳定性，即存在常数k〉0，使得对于任意ε〉0，Y∈C1[0，b]，若1yy’-1｜≤ε，y（0）=1，则存在z∈C1[a，b]满足留zz＇=1=0且：（a）=1，使得｜y（x）-z（x）｜〈Kε．

英文摘要：

The Hyers-Ulam stability of nonlinear differential equations yy＇ = 1 with initial conditions y（a）=1 was proved. It means there exists k 〉0, such that for any ε〉0,Y∈C1[0,b],whenever 1yy＇-1｜≤ε,then there exists z∈C1[a,b] with zz＇=1=0and z（a）=1,such that ｜y（x）-z（x）｜〈Kε

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期刊信息
  • 《暨南大学学报：自然科学与医学版》
  • 中国科技核心期刊
  • 主管单位:广东省教育厅
  • 主办单位:暨南大学
  • 主编：刘颖
  • 地址：广州市黄埔大道西601号
  • 邮编：510632
  • 邮箱：jdxblk@sina.com
  • 电话：020-85224092
  • 国际标准刊号：ISSN：1000-9965
  • 国内统一刊号：ISSN：44-1282/N
  • 邮发代号:46-257
  • 获奖情况:
  • 2009年全国高校科技期刊优秀编辑质量奖,2010年获教育部科技司颁发“第三届中国高校优秀期...,2011年获广东省科学技术厅“第四届广东省优秀科技...
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  • 被引量:9165