Abstract We examine the existence and uniqueness of solutions to two-point boundary value problems involving fourth-order, ordinary differential equations. Such problems have interesting applications to modelling the deflections of beams. We sharpen traditional results by showing that a larger class of problems admit a unique solution. We achieve this by drawing on fixed-point theory in an interesting and alternative way via an application of Rus’s contraction mapping theorem. The idea is to utilize two metrics on a metric space, where one pair is complete. Our theoretical results are applied to the area of elastic beam deflections when the beam is subjected to a loading force and the ends of the beam are either both clamped or one end is clamped and the other end is free. The existence and uniqueness of solutions to the models are guaranteed for certain classes of linear and nonlinear loading forces.

中文翻译：

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四阶边值问题的解和弹性梁分析的更清晰的存在性和唯一性结果

摘要 我们研究了涉及四阶常微分方程的两点边值问题解的存在性和唯一性。这些问题在模拟梁的挠度方面具有有趣的应用。我们通过展示更大类别的问题承认独特的解决方案来增强传统结果。我们通过应用 Rus 的收缩映射定理以一种有趣且替代的方式利用不动点理论来实现这一点。这个想法是在一个度量空间上使用两个度量，其中一对是完整的。我们的理论结果适用于当梁受到加载力并且梁的两端都被夹紧或一端被夹紧而另一端是自由的时弹性梁挠度的区域。