A Double S-Shaped Bifurcation Curve for a Reaction-Diffusion Model with Nonlinear Boundary Conditions
© Jerome Goddard II et al. 2010
Received: 13 November 2009
Accepted: 23 May 2010
Published: 21 June 2010
We study the positive solutions to boundary value problems of the form ; , ; , where is a bounded domain in with , is the Laplace operator, is a positive parameter, is a continuous function which is sublinear at , is the outward normal derivative, and is a smooth function nondecreasing in . In particular, we discuss the existence of at least two positive radial solutions for when is an annulus in . Further, we discuss the existence of a double S-shaped bifurcation curve when , , and with .
To access the full article, please see PDF.
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.