Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841485 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 20 Pages |
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 aa, the linear growth rate of the population, is below λ2+δλ2+δ. Here λ2λ2 is the second eigenvalue of the Dirichlet Laplacian on the domain and δ>0δ>0. Such curves have been obtained before, but only for aa in a right neighborhood of the first eigenvalue. Our analysis provides the exact number of solutions of the equation for a≤λ2a≤λ2 and new information on the number of solutions for a>λ2a>λ2.
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Pedro Martins Girão,