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

Jerome Goddard; EunKyoung Lee; R Shivaji

doi:10.1155/2010/357542

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Research Article

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

Jerome Goddard¹, EunKyoung Lee² and R Shivaji¹^*

* Corresponding author: R Shivaji shivaji@ra.msstate.edu

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

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2010/1/357542

Received:	13 November 2009
Accepted:	23 May 2010
Published:	21 June 2010

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.

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 .