Open Access Research Article

A Double S-Shaped Bifurcation Curve for a Reaction-Diffusion Model with Nonlinear Boundary Conditions

Jerome Goddard1, EunKyoung Lee2 and R Shivaji1*

Author Affiliations

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

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Boundary Value Problems 2010, 2010:357542  doi:10.1155/2010/357542

Published: 21 June 2010

Abstract

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 .