Research Article
A Double S-Shaped Bifurcation Curve for a Reaction-Diffusion Model with Nonlinear Boundary Conditions
1 Department of Mathematics and Statistics, Center for Computational Sciences, Mississippi State University, Mississippi State, MS 39762, USA
2 Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea
Boundary Value Problems 2010, 2010:357542 doi:10.1155/2010/357542
Published: 21 June 2010Abstract
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 
.
