arXiv subjects

Pedro M. Girão

Publications and source records attributed to Pedro M. Girão.

20 records · Page 2Linked to original sources

arXiv2014

Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction

We study the global bifurcation curves of a diffusive logistic equation, when harvesting is orthogonal to the first eigenfunction of the Laplacian, for values of the linear growth up to $λ_2+δ$, examining in detail their behavior as the linear growth rate crosses the first two eigenvalues. We observe some new behavior with regard to earlier works concerning this equation. Namely, the bifurcation curves suffer a transformation at $λ_1$, they are compact above $λ_1$, there are precisely two families of degenerate solutions with Morse index equal to zero, and the whole set of solutions below $λ_2$ is not a two dimensional manifold.

math.AP↗

arXiv2014

Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue

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 $a\leqλ_2$ and new information on the number of solutions for $a>λ_2$.

math.AP↗