| 一类四阶边值问题的正解的存在性与多重性 |
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| 引用本文： | 王云杰,朱江.一类四阶边值问题的正解的存在性与多重性[J].中山大学学报(自然科学版),2012,51(1):25-29. |
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| 作者姓名： | 王云杰 朱江 |
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| 作者单位： | 徐州师范大学科文学院;徐州师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(10771212);徐州师范大学自然科学基金资助项目(09KLB03) |
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| 摘 要： | 为了进一步发展和完善四阶边值问题正解的存在性理论，研究了下面的四阶边值问题{u(4) =f(t,u(t),u′(t),u″(t),u(t)),0≤t≤1
u′(0)=u″(0)=u(0)=0,
ku(1)=u(1)其中，f:［0,1］×R4→［0,+∞)连续。利用锥上不动点定理得到了该四阶边值问题正解的存在性及多重性。推广了某些已知的结果。
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| 关 键 词： | 四阶边值问题 正解的存在性 不动点定理 锥 |
| 收稿时间： | 2011-04-12; |
The Existence and Multiplicity of Positive Solutions for a Class of Fourth Order Boundary Value Problem |
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| WANG Yunjie,ZHU Jiang.The Existence and Multiplicity of Positive Solutions for a Class of Fourth Order Boundary Value Problem[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2012,51(1):25-29. |
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| Authors: | WANG Yunjie ZHU Jiang |
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| Institution: | 1.Kewen Institute of Xuzhou Normal University,Xuzhou 221116,China; 2.School of Mathematical Science,Xuzhou Normal University,Xuzhou 221116,China) |
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| Abstract: | In order to develop and improve the theory about existence of positive solutions of fourth order boundary value problem,the following fourth order boundary value problem {u(4)=f(t,u(t),u′(t),u″(t),u’’’(t)),0≤t≤1u′(0)=u″(0)=u’’’(0)=0,ku(1)=u’’’(1) is considered,where f:×R4→0,+∞) is continuous.By use of the fixed point theorem in cone,the existence and multiplicity of positive solutions are obtained to the above boundary value problem.The results generalize some recent ones. |
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| Keywords: | fourth order boundary value problem the existence of positive solutions fixed point theorem cone |
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