Abstract
The Euler buckling problem is
(E)
Even though Lu = -u″ isn’t invertible with respect to the given boundary condition, we can apply Theorem 19.9 to the modified problem
(E∈)
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 .
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© 2004 Springer Science+Business Media New York
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Brown, R.F. (2004). Euler Buckling. In: A Topological Introduction to Nonlinear Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8124-1_20
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DOI: https://doi.org/10.1007/978-0-8176-8124-1_20
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3258-8
Online ISBN: 978-0-8176-8124-1
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