Atlas home ||
Conferences |
Abstracts |
about Atlas
Eighth Mississippi State - UAB Conference on Differential Equations & Computational Simulations
May 7-9, 2009
Department of Mathematics and Statistics, Mississippi State University
Mississippi State, MS, USA |
|
Organizers
Mississippi State University & University of Alabama - Birmingham
View Abstracts
Conference Homepage |
On the existence of a double S-shaped bifurcation curve
by
Jerome Goddard, II
Department of Mathematics and Statistics, Mississippi State University
Coauthors: E. Lee (Mississippi State University),
R. Shivaji (Mississippi State University)
Abstract
We analyze the structure of the bifurcation curve of positive solutions to the two-point boundary value problem,
|
-u" = le[(bu)/(b+ u)]; (0, 1) |
|
with nonlinear boundary conditions:
| |
-a(x, u) u'+ [1 - a(x, u)]u |
|
|
| |
| |
a(x, u) u'+ [1 - a(x, u)]u |
|
|
| |
|
Here, b and l are positive parameters and a(x, u) is the fraction of what u represents that remains on the boundary. In particular, we consider the case when
| | |
| | a(x, u) = |
u
u + 1
|
; x = 1. |
| |
|
We will discuss the existence of 6 positive solutions for a certain range of l when b is sufficiently large.
PDF
Date received: April 7, 2009
Copyright © 2009 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cayt-48.