Document Type

Dissertation

Date of Degree

Spring 2011

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Yi Li

Abstract

We consider positive solutions of the nonlinear two point boundary value problem u‘‘+λf(u)=0, u(-1)=u(1)=0 , f(u)=u(u-a)(u-b)(u-c)(1-u), 0, depending on a parameter λ. Each solution u(x) is even function, and it is uniquely identified by α=u(0). We will prove, using delicate integral estimates that α=b,1 are not bifurcations points. We explore and prove a series of properties which restrict the location of a bifurcation point by studying the change of concavity of the graph of f and the points where the rays from 0 and b touche the graph of f.

Pages

iv, 58 pages

Bibliography

Includes bibliographical references (pages 57-58).

Copyright

Copyright 2011 Alvaro Ramon Correa

Included in

Mathematics Commons

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