| 摘要: |
| 考察了含有各阶导数的非线性四阶两点边值问题的解的存在性。在材料力学中该问题称为悬臂梁方程，它 描述了一端固定、另一端自由的弹桂梁的形变。利用Green函数和非线性抉择，通过构造适当的Banach空间，并且 利用积分方程技巧在非线性项满足函数型线性增长的条件下获得了该问题的一个存在定理。 |
| 关键词: 四阶常微分方程 边值问题 解的存在性 非线性抉择 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金资助项目(10571085) |
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| An existence theorem of solution to a nonlinear cantilever beam equation |
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YAO Qing-liu
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(Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003，China)
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| Abstract: |
| The existence of solution was considered for a nonlinear fourth-order two-point boundary value problem with all order derivatives. In material mechanics, the problem is called cantilever beam equation which describes the deformations of an elastic beam fixed at left and freed at right. By using Green function and nonlinear alternative, constructing suitable Banach space and applying the technique of integral equation, an existence theorem was obtained for the problem when the nonlinear term satisfies the condition of .functional linear increase. |
| Key words: fourth-order ordinary differential equation boundary value problem existence of solution nonlinear alternative |
