Global structure of the set of 1-node solutions in a class of degenerate diffusive logistic equations

Abstract

In this paper, we analyze from a numerical point of view the global structure of the set of solutions with one interior node of a degenerate diffusive logistic equation of huge interest in Population Dynamics. Our main findings reveal that the number of nodal solutions as well as the number of components in the bifurcation diagrams strongly depends on the number and position of the components where the weight function in front of the nonlinearity vanishes. No technical tool seems to be available to treat analytically these problems.