Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue
✍ Scribed by Pedro Martins Girão
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 474 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0362-546X
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✦ Synopsis
We construct the global bifurcation curves, solutions versus level of harvesting, for the steady states of a diffusive logistic equation on a bounded domain, under Dirichlet boundary conditions and other appropriate hypotheses, when a, the linear growth rate of the population, is below λ 2 + δ. Here λ 2 is the second eigenvalue of the Dirichlet Laplacian on the domain and δ > 0. Such curves have been obtained before, but only for a in a right neighborhood of the first eigenvalue. Our analysis provides the exact number of solutions of the equation for a ≤ λ 2 and new information on the number of solutions for a > λ 2 .