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

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 .

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Correspondence to R Shivaji.

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Goddard, J., Lee, E. & Shivaji, R. A Double S-Shaped Bifurcation Curve for a Reaction-Diffusion Model with Nonlinear Boundary Conditions. Bound Value Probl 2010, 357542 (2010). https://doi.org/10.1155/2010/357542

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Keywords

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