| 关于奇异二阶微分方程（Φ（X’））’＋f（t，X）＝0的某些可解准则 |
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| 引用本文： | 刘希玉.关于奇异二阶微分方程（Φ（X’））’＋f（t，X）＝0的某些可解准则[J].数学学报,1996,39(3):366-375. |
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| 作者姓名： | 刘希玉 |
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| 作者单位： | 山东师范大学数学系 |
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| 摘 要： | 本文讨论了一类右端具有奇异性的二阶常微分方程的边值问题，证明了当ｆ（ｔ，ｘ）关于ｔ的奇异程度大于某值时，边值问题无解，而当奇异程度小于某值时，边值问题有解．关于ｕ在ｕ＝０的奇异程度没有限制．
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| 关 键 词： | 奇异边值问题，逼近解，锥 |
| 收稿时间： | 1994-4-20 |
| 修稿时间： | 1994-9-8 |
Some Existence Principles for the Singular Second Order Differential Equation(Ф(x'))' + f(t, x) = 0 |
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| Liu Xiyu.Some Existence Principles for the Singular Second Order Differential Equation(Ф(x'))' + f(t, x) = 0[J].Acta Mathematica Sinica,1996,39(3):366-375. |
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| Authors: | Liu Xiyu |
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| Institution: | Liu Xiyu(Department of Mathematics, Shandong Normal University, University,Jinan 250014,China) |
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| Abstract: | This paper deals with a class of boundary value problems of ordinary differential equations of second order which have singular right hand term. We will show that there are no solutions when the singularity of f(t,x) with respect to t is greater than a certain value, and solutions exist while the singularity is less than the value. The singularity with respect to u at u = 0 is not restricted. |
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| Keywords: | singular boundary value problem approximate solutions cone |
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