Date of Degree
PhD (Doctor of Philosophy)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
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.
iv, 58 pages
Includes bibliographical references (pages 57-58).
Copyright 2011 Alvaro Ramon Correa
Correa, Alvaro. "Bifurcation theory for a class of second order differential equations." PhD (Doctor of Philosophy) thesis, University of Iowa, 2011.