| 四阶边值问题与其共轭问题正解的同时存在性 |
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| 引用本文： | 高丽新,刘进生.四阶边值问题与其共轭问题正解的同时存在性[J].太原理工大学学报,2006,37(2):233-237,241. |
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| 作者姓名： | 高丽新 刘进生 |
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| 作者单位： | 太原理工大学理学院,山西太原030024 |
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| 基金项目： | 山西省自然科学基金资助项目（20051005） |
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| 摘 要： | 研究一类非线性四阶方程边值问题与其共轭边值问题正解的同时存在性及多解性。利用两个问题相应的Green函数，将其转化为Hammerstein型积分方程，借助于锥上的不动点指数理论，结合相应线性问题的第一特征值，分别给出了两个问题单个正解与多个正解同时存在的两个充分条件。作为应用，举出了相应的实例，以说明假设条件的可实现性及合理性。
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| 关 键 词： | 四阶边值问题 共轭 正解 存在性 多解性 不动点指数 特征值 |
| 文章编号： | 1007-9432（2006）02-0233-05 |
| 收稿时间： | 2005-05-10 |
| 修稿时间： | 2005-05-10 |
The Simultaneous Existence and Multiplicity of Positive Solutions for Fourth-order Boundary Value and the Conjugate Problems |
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| GAO Li-xin, LIU Jin-sheng.The Simultaneous Existence and Multiplicity of Positive Solutions for Fourth-order Boundary Value and the Conjugate Problems[J].Journal of Taiyuan University of Technology,2006,37(2):233-237,241. |
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| Authors: | GAO Li-xin LIU Jin-sheng |
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| Institution: | Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024,China |
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| Abstract: | In this paper,the simultaneous existence and multiplicity of positive solutions for a nonlinear fourth-order boundary value and the conjugate problem are discussed.The two problems are transformed into Hammerstein integral equations with their corresponding Green's functions.By employing the fixed-point index of cone and combining with the first eigenvalue of the related linear problem,the authors present respectively two sufficient conditions for the simultaneous existence of single and multiple positive solutions to the two problems.As an application,the corresponding examples are given to demonstrate our assumptions are realizable and reasonable. |
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| Keywords: | Fourth-order boundary value problem conjugate positive solution existence multiplicity fixed-point index eigenvalue |
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