| 一类奇异4阶常微分方程的两点边值问题 |
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| 引用本文： | 姚庆六.一类奇异4阶常微分方程的两点边值问题[J].浙江大学学报(理学版),2010,37(5):497-500. |
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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 |
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| 摘 要： | 考察了4阶两点边值问题u(4)(t)=f(t,u(t),u′(t)),0t1,u(0)=u′(0)=u′(1)=u″(1)=0的正解,其中非线性项f(t,u,v)可以在t=0,t=1及u=0,v=0处奇异.结论表明这个问题可以具有1~3个正解,只要非线性项的连续部分在某些有界集上的"高度"都是适当的.
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| 关 键 词： | 奇异常微分方程 边值问题 正解 存在性 多解性 |
Two-point boundary value problems of a class of singular fourth-order ordinary differential equations |
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| YAO Qing-liu.Two-point boundary value problems of a class of singular fourth-order ordinary differential equations[J].Journal of Zhejiang University(Sciences Edition),2010,37(5):497-500. |
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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 the fourth-order two-point boundary value problemu（4）（t）=f（t,u（t）,u′（t））,0t1,u（0）=u′（0）=u′（1）=u″（1）=0,where the nonlinear term may be singular at t=0,t=1 and u=0,v=0.The results show that the problem can have 1-3 positive solutions provided that the heights of continuous part of nonlinear term are appropriate on some bounded sets. |
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| Keywords: | singular ordinary differential equation boundary value problem positive solution existence multiplicity |
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