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具积分边值条件二阶微分方程组正解的存在性 被引量：1

Existence of Positive Solutions for a System of Second Order Equations with Integral Boundary Conditions
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摘要 运用Krasnoselskii不动点定理研究具有积分边值条件的二阶微分方程组问题,得到了该问题正解的存在性及多解的存在性. This paper deals with a system of second order equations with integral boundary conditions.Using Krasnoselskii fixed point theorem,the authors obtained the existence of positive solutions and multiple solutions to the above problem.
作者 宋文晶 高文杰
机构地区 吉林大学数学研究所 吉林财经大学应用数学学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2011年第3期363-368,共6页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10771085) 吉林大学"985工程"项目基金
关键词 正解 积分边值条件 不动点定理 positive solution integral boundary condition fixed point theorem
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Cannon J R.The Solution of the Heat Equation Subject to the Specification of Energy[J].Quart Appl Math,1963,21(2):155-160.
  • 2Ionkin N I.Solution of a Boundary Value Problem in Heat Conduction Theory with Nonlocal Boundary Conditions[J].Differential Equations,1977,13:294-304.
  • 3Chegis Y R.Numerical Solution of a Heat Conduction Problem with an Integral Boundary Condition[J].Litovsk Mat Sb,1984,24:209-215.
  • 4Boucherif A.Second-Order Boundary Value Problems with Integral Boundary Conditions[J].Nonlinear Analysis:Theory,Methods & Applications,2009,70(1):364-371.
  • 5马琦,高文杰.一类非线性奇异边值问题多重正解的存在性[J].吉林大学学报（理学版）,2004,42(1):1-5. 被引量：11
  • 6李圆晓,魏英杰,高文杰.拟线性二阶方程三点边值问题对称正解的存在性[J].吉林大学学报（理学版）,2010,48(1):1-8. 被引量：2
  • 7LIU Bing-mei,LIU Li-shan,WU Yong-hong.Positive Solutions for Singular Systems of Three-Point Boundary Value Problems[J].Computers and Mathematics with Applications,2007,53 (9):1429-1438.
  • 8LIU Li-shan,KANG Ping,WU Yong-hong,et al.Positive Solutions of Singular Boundary Value Problems for Systems of Nonlinear Fourth Order Differential Equations[J].Nonlinear Analysis:Theory,Methods & Applications,2008,68(3):485-498.
  • 9YANG Zhi-lin.Positive Solutions to a System of Second-Order Nonlocal Boundary Value Problems[J].Nonlinear Anal,2005,62(17):1251-1265.
  • 10ZHANG Xue-mei,GE Wei-gao.Positive Solutions for a Class of Boundary-Value Problems with Integral Boundary Conditions[J].Computers Mathematics with Applications,2009,58 (2):203-215.

二级参考文献16

  • 1李翠哲 葛渭高.Positive solutions to a singular Sturm-Liouville boundary value problems for the one-dimensional p-Laplacian equation(一维p-Laplacian奇异Sturm-Liouville边值问题的正解) [J].Appl Math,.
  • 2刘斌 庾建设.Multiple positive solutions to a singular boundary value problem for a p-Laplacian type equation(具p-Laplace算子型奇异边值问题多重正解) [J].Chinese Ann Math(数学年刊),2001,22(6):721-72.
  • 3II'in V A, Moiseer E I. Nonlocal Boundary Value Problem of the First Kind for a Sturm-Liouville Operator in Its Differential and Finite Difference Aspects [ J]. Differ Equ, 1987, 23(7) : 803-810.
  • 4II'in V A, Moiseer E I. Nonlocal Boundary Value Problem of the Second Kind for a Sturm-Liouville Operator [ J ]. Differ Equ, 1987, 23(8) : 979-987.
  • 5Henderson J, Thompson H B. Multiple Symmetric Positive Solutions for a Second Order Boundary Value Problem [J]. Proc Amer Math Soc, 2000, 128(8) : 2573-2579.
  • 6LI Fu-yi, ZHANG Ya-jing. Muhiple Symmetric Nonnegative Solutions of Second Order Ordinary Differential Equations [J]. Appl Math Lett, 2004, 17(3) : 261-267.
  • 7YAO Qing-liu. Existence and Iteration of n Symmetric Positive Solutions for a Singular Two-Point Boundary Value Problem [J]. Comput Math Appl, 2004, 47(8/9) : 1195-1200.
  • 8SUN Yong-ping. Optimal Existence Criteria for Symmetric Positive Solutions to a Three-Point Boundary Value problem [J]. Nonlinear Anal, 2007, 66(5) : 1051-1063.
  • 9Kosmatov N. Symmetric Solutions of a Multi-Point Boundary Value Problem [ J ]. J Math Anal Appl, 2005, 309 ( 1 ) : 25 -36.
  • 10Avery R I, Peterson A C. Three Positive Fixed Point of Nonlinear Operators on Ordered Banacli Spaces [ J ]. Comput Math Appl, 2001, 42(3/4/5) : 313-322.

共引文献11

同被引文献9

  • 1Cannon J R. The Solution of the Heat Equation Subject to the Specification of Energy [J]. Quart Appl Math, 1963, 21(2): 155-160.
  • 2Ionkin N I. Solution of a Boundary Value Problem in Heat Conduction Theory with Nonlocal Boundary Conditions [J]. Differential Equations, 1977, 13: 294-304.
  • 3Chegis R Y. Numerical Solution of a Heat Conduction Problem with an Integral Boundary Condition [J]. Litovsk Mat Sb, 1984, 24: 209-215.
  • 4WANG You-yu, GE Wei-gao. Existence of Solutions for a Third Order Differential Equation with Integral Boundary Conditions [J]. Comput Math Appl, 2007, 53(1) : 144-154.
  • 5WANG You-yu, I.IU Guo-feng, HU Yin-ping. Existence and Uniqueness of Solutions for a Second Order Differential Equation with Integral Boundary Conditions [J]. Appl Math Comput, 2010, 216(9): 2718-2727.
  • 6Boucherif A. Second-Order Boundary Value Problems with Integral Boundary Conditions [J]. Nonlinear Anal: Theory, Methods & Applications, 2009, 70(1): 364-371.
  • 7Ahmad B, Alsaedi A, Alghamdi B S. Analytic Approximation of Solutions of the Forced Dulling Equation with Integral Boundary Conditions[J].Nonlinear Anal Real World Applications, 2008, 9(4): 1727-1740.
  • 8YANG Zhi-lin. Positive Solutions to a System of Second Order Nonlocal Boundary Value Problems [J]. Nonlinear Anal: Theory, Methods & Applications, 2005, 62(7): 1251-1265.
  • 9张兴秋.奇异四阶积分边值问题正解的存在唯一性[J].应用数学学报,2010,33(1):38-50. 被引量：6

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吉林大学学报（理学版）
2011年 第3期

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