| 非线性项含有变号一阶导数的四阶边值问题 |
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| 引用本文： | 姚庆六.非线性项含有变号一阶导数的四阶边值问题[J].滨州学院学报,2012(6):1-6. |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | 南京财经大学应用数学系,江苏南京210003 |
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| 基金项目： | 国家自然科学基金资助项目（11071109） |
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| 摘 要： | 考察了一个四阶两点边值问题的正解,它的非线性项含有变号的一阶导数.通过利用锥压缩与锥拉伸型的Krasnosel′skii不动点定理证明了几个存在性与多解性定理.特别地,只要非线性项的主要部分在某些有界集合上的高度适当,这个问题能够具有n个正解,其中n是一个任意的自然数.
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| 关 键 词： | 非线性常微分方程 边值问题 正解 存在性与多解性 |
A Fourth-Order Boundary Value Problem whose Nonlinearity Contains Changing-Sign First Derivative |
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| YAO Qing-liu.A Fourth-Order Boundary Value Problem whose Nonlinearity Contains Changing-Sign First Derivative[J].Journal of Binzhou University,2012(6):1-6. |
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| Authors: | YAO Qing-liu |
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| Institution: | YAO Qing-liu (Department of Applied Mathematics, Nanjing University of Finance and Economics ,Nanjing 210003,China) |
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| Abstract: | The positive solutions are considered for a fourth-order two-point boundary value problem whose nonlinearity contains changing-sign first derivative. By applying the Krasnosellskii fixed point theorem of cone expansion-compression type,several existence and multiplicity theorems are proved. Particularly,the problem can have n positive solutions if the heights of principle part of nonlinearity are appropriate on some bounded sets. Here n is an arbitrary natural number. |
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| Keywords: | nonlinear ordinary differential equation boundary value problem positive solution existence multiplicity |
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