Date of Degree
2011
Document Type
dissertation
Degree Name
PhD (Doctor of Philosophy)
Department
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
Bibliography
57-58
Copyright
Copyright 2011 Alvaro Ramon Correa
Recommended Citation
Correa, Alvaro. "Bifurcation theory for a class of second order differential equations." doctoral dissertation, University of Iowa, 2011.
http://ir.uiowa.edu/etd/940.