Phd records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:19:47 +0000Bifurcation theory of nonlinear boundary value problems
https://resolver.caltech.edu/CaltechTHESIS:04082013-100223262
Authors: {'items': [{'id': 'Langford-W-F', 'name': {'family': 'Langford', 'given': 'William Finlay'}, 'show_email': 'NO'}]}
Year: 1971
DOI: 10.7907/BP03-ZM29
<p>The theory of bifurcation of solutions to two-point boundary
value problems is developed for a system of nonlinear first order
ordinary differential equations in which the bifurcation parameter is
allowed to appear nonlinearly. An iteration method is used to
establish necessary and sufficient conditions for bifurcation and to
construct a unique bifurcated branch in a neighborhood of a bifurcation
point which is a simple eigenvalue of the linearized problem. The
problem of bifurcation at a degenerate eigenvalue of the linearized
problem is reduced to that of solving a system of algebraic equations.
Cases with no bifurcation and with multiple bifurcation at a
degenerate eigenvalue are considered.</p>
<p>The iteration method employed is shown to generate
approximate solutions which contain those obtained by formal
perturbation theory. Thus the formal perturbation solutions are
rigorously justified. A theory of continuation of a solution branch
out of the neighborhood of its bifurcation point is presented. Several
generalizations and extensions of the theory to other types of
problems, such as systems of partial differential equations, are
described.</p>
<p>The theory is applied to the problem of the axisymmetric
buckling of thin spherical shells. Results are obtained which
confirm recent numerical computations.</p>https://thesis.library.caltech.edu/id/eprint/7584