Euler Buckling

Robert F. Brown
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Robert F. Brown: University of California, Department of Mathematics

Chapter 20 in A Topological Introduction to Nonlinear Analysis, 2004, pp 155-160 from Springer

Abstract: Abstract The Euler buckling problem is $$ - u'' = \lambda \sin u, $$ (E) $$ u'(0) = u'(\pi ) = 0. $$ Even though Lu = -u″ isn’t invertible with respect to the given boundary condition, we can apply Theorem 19.9 to the modified problem $$ - u'' - \in u = \lambda \sin u, $$ (E∈) $$ u'(0) = u'(\pi ) = 0 $$ to prove Theorem 20.1. For each k = 1, 2, …, the integer k2 is a bifurcation point for the Euler buckling problem (E) and the branch C k of nontrivial solutions containing (k2, 0) is an unbounded subset of R × X such that if(λ, u) ∈ C k with u ≠ 0, then u ∈ S k .

Keywords: Shape Function; Constant Function; Bifurcation Point; Nontrivial Solution; Tangent Line (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8124-1_20

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