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  • Research Article
  • Open Access

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

Boundary Value Problems20102010:357542

  • Received: 13 November 2009
  • Accepted: 23 May 2010
  • Published:


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 .


  • Boundary Condition
  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation

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Authors’ Affiliations

Department of Mathematics and Statistics, Center for Computational Sciences, Mississippi State University, Mississippi State MS 39762, USA
Department of Mathematics, Pusan National University, Busan, 609-735, Republic of Korea


© Jerome Goddard II et al. 2010

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.