| 二阶积分-微分方程周期边值问题解的存在性 |
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| 引用本文： | 周媛媛,刘文斌.二阶积分-微分方程周期边值问题解的存在性[J].徐州师范大学学报(自然科学版),2013(1):8-14. |
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| 作者姓名： | 周媛媛 刘文斌 |
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| 作者单位： | [1]江苏师范大学科文学院,江苏徐州221116 [2]中国矿业大学理学院,江苏徐州221008 |
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| 基金项目： | 国家自然科学基金资助项目（10771212） |
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| 摘 要： | 利用半序理论及单调迭代方法研究了实Banach空间中二阶非线性混合型积分一微分方程周期边值问题，其中相应的下解a和上解卢不必满足边界条件：α′（0）≥α′（2π），β′（0）≤β′（2π）,对于下解α与上解卢的两种情形：α≤β或β≤α，均建立了最大解和最小解的存在性定理．
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| 关 键 词： | 周期边值问题 上下解 反向上下解 |
Existence of solutions for PBVP of second order integro-differential equations |
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| Zhou Yuanyuan,Liu Wenbin.Existence of solutions for PBVP of second order integro-differential equations[J].Journal of Xuzhou Normal University(Natural Science Edition),2013(1):8-14. |
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| Authors: | Zhou Yuanyuan Liu Wenbin |
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| Institution: | 1. Kewen Institute, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China 2. School of Sciences, China University of Mining 8〈 Technology, Xuzhou 221008 ,Jiangsu,China) |
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| Abstract: | Combining the semi-order theory with monotone iterative technique,the PBVP for second order nonlinear integro-differential equations of mixed type in Banach space are investigated, where the corresponding lower and up-per solutions α,β do not necessarily satisfy the boundary conditions：α′（0）≥α′（2π）,β′（0）≤β′（2π）. For two situa-tions relative to lower and upper solutions α≤β or β≤α the existence theorems on their maximal and minimal solutions are established. |
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| Keywords: | periodic boundary value problem（PBVP） upper and lower solution upper and lower solution in the re-versed order |
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