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三阶三点边值问题解的存在性与唯一性 被引量：1

Existence and uniqueness of solutions of third-order three-point boundary value problems with upper and lower solutions in the reversed order
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摘要 研究了反序上下解条件下三阶微分方程三点边值问题解的存在性与唯一性.利用单调迭代方法,分别得到解存在与唯一的充分条件,在满足解的唯一性的条件下,给出了求解的迭代序列及误差估计式. The existence and uniqueness of solutions of third-order three-points boundary value problems with lower and upper solutions were studied. The sufficient conditions for the existence and uniqueness of solutions were provided by use of the monotone iterative method in the reversed order. The iterative sequence for solving a solution and its error estimate formula under the condition of unique solution were presented.
作者 纪慧鹏 贾梅 席守亮
机构地区 上海理工大学理学院
出处 《上海理工大学学报》 CAS 北大核心 2009年第6期511-516,共6页 Journal of University of Shanghai For Science and Technology
基金 上海市教委科研创新基金重点资助项目(10ZZ93)
关键词 边值问题 单调迭代方法 反序上下解 存在性与唯一性 误差估计 boundary value problem monotone iterative method upper and lower solutions in reversed order existence and uniqueness error estimate
分类号 O175.08 [理学—基础数学]
  • 相关文献

参考文献9

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二级参考文献11

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共引文献5

同被引文献7

  • 1郭大钧,孙经先,刘兆理.非线性常微分方程泛函方法[M].2版.济南:山东科学技术出版社,2006.
  • 2LI Fang-fei, SUN Ji-tao, JIA Mei. Monotone Iterative Method for the Second-Order Three-Point Boundary Value Problem with Upper and Lower Solutions in the Reversed Order [J]. Appl Math Comp, 2011, 217(9): 4840-4847.
  • 3LI Fang-fei, JIA Mei, LIU Xi-ping, et al. Existence and Uniqueness of Solutions of Second-Order Three-Point Boundary Value Problems with Upper and Lower Solutions in the Reversed Order [J]. Nonlinear Anal: Theory, Methods ~ Applications, 2008, 68: 2381-2388.
  • 4Cabada A, Grossinho M R, Minh6s F M. Extremal Solutions for Third-Order Nonlinear Problems with Upper and Lower Solutions in Reversed Order [J]. Nonlinear Anal: Theory, Methods & Applications, 2005, 62(6): 1109-1121.
  • 5Cabada A, Pouso R L, Minhos F M. Extremal Solutions to Fourth-Order Functional Boundary Value Problems Including Muhipoint Conditions ~J]. Nonlinear Anal Real World Appl, 2009, 10(4):2157-2170.
  • 6敖婧,张然,张凯.一类二阶四点边值问题解的存在性[J].吉林大学学报（理学版）,2008,46(2):173-178. 被引量：1
  • 7刘颖.n阶非线性微分方程的三点及四点边值问题[J].吉林大学学报（理学版）,2002,40(1):10-15. 被引量：2

引证文献1

上海理工大学学报
2009年 第6期

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