On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains

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We study a diffusive logistic equation with nonlinear boundary conditions. The equation arises as a model for a population that grows logistically inside a patch and crosses the patch boundary at a rate that depends on the population density. Specifically, the rate at which the population crosses the boundary is assumed to decrease as the density of the population increases. The model is motivated by empirical work on the Glanville fritillary butterfly. We derive local and global bifurcation results which show that the model can have multiple equilibria and in some parameter ranges can support Allee effects. The analysis leads to eigenvalue problems with nonstandard boundary conditions.

Original languageEnglish (US)
Pages (from-to)768-804
Number of pages37
JournalJournal of Differential Equations
Issue number2
StatePublished - Dec 15 2006



  • Allee effect
  • Bifurcation
  • Eigenvalue problems
  • Logistic equation
  • Nonlinear boundary conditions
  • Reaction-diffusion

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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