  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
$\lambda_2+\delta$. Here $\lambda_2$ is the second eigenvalue of the Dirichlet
Laplacian on the domain and $\delta>0$. 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 $a\leq\lambda_2$ and
new information on the number of solutions for $a>\lambda_2$.
