| 不连续三阶两点边值问题的可解性 |
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| 引用本文： | 姚庆六.不连续三阶两点边值问题的可解性[J].应用数学,2007,20(3):458-461. |
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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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| 摘 要： | 证明了非线性三阶两点边值问题u′″（t）-q（u″（t））f（t，u（t）），u（O）=a，u（1）=b，u″（0）=c解的一个存在定理．在这个问题中，f（t，u）是一个Carathéodory函数而边界条件是非齐次的．我们的结论表明该问题能够有一个解，只要在R。的某个有界集合上q（υ）的“本性高度”与f（t，u）的“最大高度”积分的乘积是适当的．
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| 关 键 词： | 非线性三阶常微方程 非齐次两点边值问题 奇异性 解 存在性 |
| 文章编号： | 1001-9847（2007）03-0458-04 |
Solvability of Discontinuous Third-order Two-point Boundary Value Problems |
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| YAO Qing-liu.Solvability of Discontinuous Third-order Two-point Boundary Value Problems[J].Mathematica Applicata,2007,20(3):458-461. |
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| Authors: | YAO Qing-liu |
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| Institution: | Department of Applied Mathematics, Nanjing Nanjing 210003 ,China |
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| Abstract: | An existence theorem of solution is proved for the nonlinear third-order two-point boundary value problem u′′′(t)=q(u′′(t))f(t,u(t)),u(0)=a,u(1)=b,u′′(0)=c. In this problem,f(t,u) is a Carathéodory function and the bounded condition is nonhomogeneous.Our result shows that the problem can have a solution provided the product of "essential height" of q(v) and integration of "maximum height" of f(t,u) is appropriate on certain bounded subset of R3. |
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| Keywords: | Nonlinear third-order ordinary differential equation Nonhomogeneous two-point boundary value problem Singularity Solution Existence |
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