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:10.1155/2010/357542Published: 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 .