Boundary value problems and bifurcation theory for ordinary differential equations Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/000003068

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  • Two numerical methods are presented that can be used to solve second order nonlinear ordinary differential equations with periodic boundary conditions. One of these methods is a shooting method developed solely for the periodic problem. The other, "quasilinearization," is a method applicable to a wide variety of problems. It is presented in a quite general setting; and then is used to solve the periodic problem. Under suitable hypotheses both methods are shown to converge. Numerical results are given. Secondly, we prove bifurcation of solutions of nonlinear Sturm-Liouville problems as well as some related global results. The approach used does not use degree theory, Liaupunov- Schmidt theory, or functional analysis; but instead, elementary facts about continuous functions and differential equations.
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