| Banach空间二阶积-微分方程两点边值问题解的存在性 |
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| 引用本文： | 刘晓亚,王锐利.Banach空间二阶积-微分方程两点边值问题解的存在性[J].河南师范大学学报(自然科学版),2011,39(4):14-17. |
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| 作者姓名： | 刘晓亚 王锐利 |
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| 作者单位： | 1. 西北师范大学数学与信息科学学院,兰州,730070
2. 济源职业技术学院建筑工程系,河南济源,454650 |
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| 基金项目： | 国家自然科学基金(10871160); 西北师范大学创新工程(NWNU-KJCXGC-3-47) |
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| 摘 要： | 利用上下解的单调迭代技巧讨论了Banach空间二阶积-微分方程两点边值问题-u″(t)=f(t,u(t),Su(t)),t∈I,u(0)=u(1)=θ解的存在性.其中f∈C(I×E×E,E),I=0,1].在非线性项f满足一定的非紧性测度条件和单调性条件下,利用相应的线性方程解算子的谱半径,通过非紧性测度的精细计算,获得了其在上下解之间的最小、最大解的存在性以及在上下解之间解的唯一性.
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| 关 键 词： | 积-微分方程 边值问题 锥 上下解 非紧性测度 |
Existence of Solutions of Two-point Boundary Value Problem for Sencond-order Integro-differential Equations in Banach Spaces |
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| LIU Xiao-ya,WANG Rui-li.Existence of Solutions of Two-point Boundary Value Problem for Sencond-order Integro-differential Equations in Banach Spaces[J].Journal of Henan Normal University(Natural Science),2011,39(4):14-17. |
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| Authors: | LIU Xiao-ya WANG Rui-li |
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| Institution: | LIU Xiao-ya,WANG Rui-li2(1.College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China,2.Department of Architectural Engineering,Jiyuan Vocational and Technical College,Jiyuan 454650,China) |
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| Abstract: | This research uses a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of solutions for two-point boundary value problem of sencond-order integro-differential equations in Banach space E-u″(t)=f(t,u(t),Su(t)),t∈I,u(0)=u(1)=θ,where f∈C(I×E×E,E),I=.Under wide monotone conditions and the noncompactness measure condition of nonlinearity f,using the spectral radius of the solving operator for corresponding linear equations and more accurate computation of measure of noncompactness,the existence of extremal solutions and unique solution between lower and upper solutions are obtained. |
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| Keywords: | integro-differential equations boundary value problem cone lower and upper solutions measure of noncompactness |
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