临界锥杆的屈曲:解的一些整体分支的性质

C. Stuart, G. Vuillaume
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引用次数: 12

摘要

本文是C. a . Stuart & G. Vuillaume (2003 Proc. R. Soc)的延续。Lond。A459, 1863-1889),是关于锥形棒的屈曲的研究。这种物理现象导致非线性特征值问题:{A(s)u'(s)}'+μsinu(s)=0s∈(0,1),u(1)= lims→0A(s) u'(s)=0∫1 A(s)u'(s) 2 ds 0对于所有s > 0和lims→0A(s)/sp = L对于某些常数p大于或等于0和L ε(0,∞)。我们处理了临界情况p= 2,并研究了问题所有解的集合。在Stuart & Vuillaume(2003)中,在A的附加假设下,我们发现了点{μi, i ε i⫅N* ={1,2,3,…}}∧R+使得非平凡解的全局分支从每个μi, ε i中发散出来,在本文中,我们提供了关于这些解的全局分支的更详细的信息。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Buckling of a critically tapered rod: properties of some global branches of solutions
This paper, which is a continuation of C. A. Stuart & G. Vuillaume (2003 Proc. R. Soc. Lond. A459, 1863–1889), is concerned with the study of the buckling of a tapered rod. This physical phenomenon leads to the nonlinear eigenvalue problem: {A(s)u'(s)}'+μsinu(s)=0s∈(0,1), u(1)= lim s→0 A(s)u'(s)=0 ∫ 0 1 A(s)u' (s) 2 ds <∞, where A(s) ε C([0,1]) is such that A(s) > 0 for all s > 0 and lims→0A(s)/sp = L for some constants p ⩾ 0 and L ε (0,∞). We deal with the critical case p= 2 and study the set of all the solutions of the problem. In Stuart & Vuillaume (2003) and under additional assumptions on A, we found a set of points {μi , i ε I ⫅ N* ={1,2,3,...}} ⊂ R+ such that a global branch of non–trivial solutions emanates from each μi , iε I. In this paper, we provide more detailed information about these global branches of solutions.
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期刊介绍: Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.
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