Numerical continuation and the Gelfand problem

This paper examines a semilinear elliptic equation with nonlinear forcing known as the Gelfand equation. Information about the solution set in terms of the parameter is determined. We are specifically interested in determining the first two ''turning points'' of the solution continuum. The primary technique is a numerical method known as pseudo-arclength continuation. This is applied to the problem to determine the ''bifurcation'' diagram for three dimensional domains.