| 奇异三阶两点边值问题解的一个存在定理 |
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| 引用本文： | 姚庆六.奇异三阶两点边值问题解的一个存在定理[J].数学季刊,2008,23(1):61-66. |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | YAO Qing-liu（Department of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210003,China） |
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| 摘 要： | By constructing suitable Banach space.an existence theorem is established under a condition of linear growth for the third-order boundary value problem u'"(t) f(t,u(t),t'(t),u"(t))=0,0＜t＜1,u(0)=u'(0)=u'(1)=0,where the nonlinear term contains first and second derivatives of unknown function.In this theorem the nonlinear term f(t,u,v,w)may be singular at t=0 and t=1.The main ingredient is Leray-Schauder nonlinear alternative.
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| 关 键 词： | singular ordinary differential equation boundary value problem existence theorem nonlinear alternative 两点边值 题解 存在定理 Boundary Value Problem Singular Solution ingredient nonlinear alternative singular existence theorem nonlinear term derivatives function established condition growth boundary value problem constructing Banach space |
| 文章编号： | 1002-0462(2008)01-0061-06 |
| 修稿时间： | 2005年6月8日 |
An Existence Theorem of Solution for a Singular Third-order Two-point Boundary Value Problem |
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| YAO Qing-liu.An Existence Theorem of Solution for a Singular Third-order Two-point Boundary Value Problem[J].Chinese Quarterly Journal of Mathematics,2008,23(1):61-66. |
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| Authors: | YAO Qing-liu |
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| Institution: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003,China |
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| Abstract: | By constructing suitable Banach space.an existence theorem is established under a condition of linear growth for the third-order boundary value problem u'"(t) f(t,u(t),t'(t),u"(t))=0,0＜t＜1,u(0)=u'(0)=u'(1)=0,where the nonlinear term contains first and second derivatives of unknown function.In this theorem the nonlinear term f(t,u,v,w)may be singular at t=0 and t=1.The main ingredient is Leray-Schauder nonlinear alternative. |
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| Keywords: | singular ordinary differential equation boundary value problem existence theorem nonlinear alternative |
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