| 含各阶导数的非线性弹性梁方程的一个存在定理 |
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| 引用本文： | 姚庆六.含各阶导数的非线性弹性梁方程的一个存在定理[J].数学研究,2005,38(1):24-28. |
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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,南京,210003 |
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| 摘 要： | 通过选择适当的Banach空间并利用Leray-Schauder非线性抉择对于含各阶导数的非线性弹性梁方程{u(4)(t)=f(t,u(t),u′(t),u″(t),u′″(t)),0≤t≤1, u(0)=u′(1)=u″(0)=u′″(1)=0.建立了一个解的存在定理．在材料力学中，该方程描述了一端简单支撑，另一端被滑动夹子夹住的弹性梁的形变．这个存在定理说明只要非线性项满足某种线性增长条件该方程至少有一个解．
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| 关 键 词： | 非线性弹性梁方程 边值问题 存在性 |
An Existence Theorem for a Nonlinear Elastic Beam Equation with All Order Derivatives |
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| Yao Qingliu.An Existence Theorem for a Nonlinear Elastic Beam Equation with All Order Derivatives[J].Journal of Mathematical Study,2005,38(1):24-28. |
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| Authors: | Yao Qingliu |
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| Abstract: | By choosing suitable Banach space and applying Leray-Schauder Nonlinear Alternative, an existence theorem of solutions is established for the nonlinear elastic beam equation with all order derivatives{u(4)(t)=f(t,u(t),u'(t),un(t),um(t),0≤t≤1,u(0)=u'(1)=u"(0)=u(')(1)=0.In the material mechanics, the equation describes the deformation of an elastic beam whose one end is simply supported and the other is clamped by sliding clamps. The existence theorem shows that the equation has at least one solution provided the nonlinear term satisfies a linear growth condition. |
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| Keywords: | Nonlinear elastic beam equation Boundary value probl em Existence |
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