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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 u0, then uS k .

Keywords

Shape Function Constant Function Bifurcation Point Nontrivial Solution Tangent Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Robert F. Brown
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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