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关于Feigenbaum型泛函方程的C^1解 被引量：3

On the C^1 Solution of the Feigenbaum Type Functional Equation
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摘要 利用Schauder不动点定理、自同胚和紧凸子集的相关性质研究Feigenbaum型泛函方程的连续可微解的存在性和唯一性. By using the Schauder fixed point theorem,self-diffeomorphism and the related properties of compact convex subset,the existence and uniqueness of the C1 solutions of the Quasi-Feigenbaum Equations are discussed.
作者 林雪梅 黄上梅 黄海敏 李晓培
机构地区 湛江师范学院数学与计算科学学院
出处 《湛江师范学院学报》 2011年第3期33-37,共5页 Journal of Zhanjiang Normal College
关键词 Feigenbaum型泛函方程 SCHAUDER不动点定理 自同胚 紧凸子集 存在性 唯一性 Feigenbaum type functional equation Schauder fixed point theorem self-diffeomorphism compact convex subset the existence and uniqueness of C1 solution continuous dependence
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献13

  • 1李晓培,邓圣福.DIFFERENTIABILITY FOR THE HIGH DIMENSIONAL POLYNOMIAL-LIKE ITERATIVE EQUATION[J].Acta Mathematica Scientia,2005,25(1):130-136. 被引量：9
  • 2李晓培.Banach空间上的一类映射迭代方程[J].四川大学学报（自然科学版）,2004,41(3):505-510. 被引量：4
  • 3张伟年.STABILITY OF THE SOLUTION OF THE ITERATED EQUATION sum from i=1 to n λ_if(x)=F(x)[J]Acta Mathematica Scientia,1988(04).
  • 4张伟年.DISCUSSION ON THE ITERATED EQUATION ■(x)=F(x)[J].Chinese Science Bulletin,1987,32(21):1444-1451. 被引量：5
  • 5Colin J. Thompson,J. B. McGuire.Asymptotic and essentially singular solutions of the Feigenbaum equation[J]. Journal of Statistical Physics . 1988 (5-6)
  • 6Jean-Pierre Eckmann,Peter Wittwer.A complete proof of the Feigenbaum conjectures[J]. Journal of Statistical Physics . 1987 (3-4)
  • 7H. Epstein.New proofs of the existence of the Feigenbaum functions[J]. Communications in Mathematical Physics . 1986 (3)
  • 8Patrick J. McCarthy.The general exact bijective continuous solution of Feigenbaum’s functional equation[J]. Communications in Mathematical Physics . 1983 (3)
  • 9Lanford O E.A computer assisted proof of the Feigenbaum conjectures. Bulletin of the American Mathematical Society . 1987
  • 10Zhang W N.Discussion on the differentiable solutions of the iterated equation∑λifi (x)=F (x). Nonlinear Analysis:Theory,Mathods and Applications . 1998

二级参考文献17

  • 1司建国.迭代方程λ_if^i(z)=F(z)局部解析解的存在性[J].数学学报（中文版）,1994,37(5):590-600. 被引量：9
  • 2司建国.一类迭代方程C^1类解的讨论[J].数学学报（中文版）,1996,39(2):247-256. 被引量：10
  • 3赵立人.关于函数方程λ1f(x)+λ2f^2(x)=F(x)解的存在唯一性定理[J].中国科技大学学报（数学专辑）,1983,:21-27.
  • 4张伟年.关于迭代方程∑i=1^nλif^i(x)=F(x)解存在性的讨论[J].科学通报,1986,31(17):1290-1295.
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  • 10Kuczma M. Functional equations in a single variable[M]. Warszawa:PWN-Polish Scientific Publishing, 1968.

共引文献14

同被引文献9

  • 1Colin J. Thompson,J. B. McGuire.Asymptotic and essentially singular solutions of the Feigenbaum equation[J]. Journal of Statistical Physics . 1988 (5-6)
  • 2H. Epstein.New proofs of the existence of the Feigenbaum functions[J]. Communications in Mathematical Physics . 1986 (3)
  • 3Patrick J. McCarthy.The general exact bijective continuous solution of Feigenbaum’s functional equation[J]. Communications in Mathematical Physics . 1983 (3)
  • 4Oscar E. Lanford III.A computer-assisted proof of the Feigenbaum conjectures[J]. Bulletin of the American Mathematical Society (1979-present) . 1982 (3)
  • 5Alexei V. Tsygvintsev,Ben D. Mestel,Andrew H. Osbaldestin.Continued fractions and solutions of the Feigenbaum-Cvitanovi\’c equation. C. R., Math., Acad. Sci. Paris . 2002
  • 6Zhang J Z,Yang L.Disscussion on iterative roots of continuous and piecewise monotone fuctions. Acta mathematica Sinica,Chinese . 1983
  • 7贺天兰.一类差分方程的不变曲线分枝[J].应用数学和力学,2001,22(9):988-996. 被引量：1
  • 8张伟年.DISCUSSION ON THE ITERATED EQUATION ■(x)=F(x)[J].Chinese Science Bulletin,1987,32(21):1444-1451. 被引量：5
  • 9李晓培.Banach空间上的一类映射迭代方程[J].四川大学学报（自然科学版）,2004,41(3):505-510. 被引量：4

引证文献3

湛江师范学院学报
2011年 第3期

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