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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

https://doi.org/10.1155/2010/357542

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

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 .

Keywords

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

Publisher note

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Authors’ 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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