Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue |
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Authors: | Pedro Martins Girão |
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Institution: | Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal |
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Abstract: | 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 λ2+δ. Here λ2 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≤λ2 and new information on the number of solutions for a>λ2. |
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Keywords: | 35B32 35J66 37B30 92D25 |
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