| 基于变分方法的四阶边值问题的多重正解 |
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| 引用本文： | 武华华,孙苏菁.基于变分方法的四阶边值问题的多重正解[J].山东科技大学学报(自然科学版),2014(2):96-99. |
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| 作者姓名： | 武华华 孙苏菁 |
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| 作者单位： | [1]山东科技大学数学与系统科学学院,山东青岛266590 [2]山东科技大学信息科学与工程学院,山东青岛266590 |
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| 基金项目： | 山东省高等学校科研计划项目（J11LA07） |
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| 摘 要： | 研究了一类弹性梁形变过程中产生的四阶微分方程边值问题,主要通过变分方法和极值原理在此类四阶微分方程正解的存在性和多重性的应用,借助山路引理的基本结论,得到所研究问题至少存在两个正解的结果。
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| 关 键 词： | 边值问题 变分方法 正解 极值原理 |
Multiple Positive Solutions for a Fourth Order Boundary Value via Variational Method |
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| Wu Huahua,Sun Sujing.Multiple Positive Solutions for a Fourth Order Boundary Value via Variational Method[J].Journal of Shandong Univ of Sci and Technol: Nat Sci,2014(2):96-99. |
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| Authors: | Wu Huahua Sun Sujing |
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| Institution: | 1. College of Mathematics and Systems Science,Shandong University of Science and Technology, Qingdao, Shandong 266590, China ; 2. College of Information Science and Engineering,Shandong University of Science and Technology, Qingdao, Shandong 266590,China) |
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| Abstract: | The paper studied a fourth order differential equation produced in process of elastic beam deformation with boundary value conditions. It applied mainly the variational method and the maximum principle in the existence and multiplicity of positive solutions for such fourth-order differential equations. The results show that there are at least two positive solutions by using the basic conclusion of mountain pass theorem. |
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| Keywords: | boundary value problems variational methods positive solutions maximum principle |
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