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Column BucklingAn Elementary Example
Bifurcation Theory for Ordinary differential
Existence of Buckled States of Circular Plates
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amplitude assume Banach space bifurcation equation bifurcation problem bifurcation theory boundary conditions boundary value problem bounded buckling calculus of variations coefficients compact concave consider constant convergence convex Corollary corresponding Couette flow curve cylinder defined denote eigenfunction eigenvalue problem elastic elliptic equa Example existence Figure finite flow fluid formulation free surface given Green's function Hilbert space homogeneous implies integral ir/n Lecture linear operator linearized equations linearized problem lower semi-continuous mapping Math minimal positive solution monotone multiplicity nonlinear nonlinear equation nonnegative nontrivial solutions norm obtain operator equation ordinary differential equations orthogonal parameter partial differential periodic solutions perturbation Positivity Lemma Proof result satisfy Section self-adjoint sequence shown solution of 3.1 solved space H sufficiently small symmetry Theorem tions torus trivial solution unique variational problem vector velocity waves x e 3D yields zero