Bifurcation Theory and Nonlinear Eigenvalue Problems |
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Contents
Column BucklingAn Elementary Example | 3 |
Bifurcation Theory for Ordinary differential | 15 |
Existence of Buckled States of Circular Plates | 49 |
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amplitude assume Banach space bifurcation equation bifurcation theory boundary conditions boundary value problem bounded buckled 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 free surface given Green's function Hilbert space implies integral L₁u L₂u L₂u,u Lecture Let f(x linear operator linearized equations linearized problem Lyusternik-Schnirelmann category mapping Math minimal positive solution monotone multiplicity nonlinear nonnegative nontrivial solutions norm obtain operator equation ordinary differential equations P₂ parameter periodic solutions perturbation Positivity Lemma Proof quasiperiodic result satisfy Section self-adjoint sequence shown solution of 3.1 solved space H sufficiently small symmetry t₁ t₂ Theorem tions trivial solution U₁ unique variational problem vector waves yields zero