Chebfun approximation to structure of positive radial solutions for a class of supercritical semi-linear Dirichlet problems

Abstract

We use the Chebfun programming package to approximate numerically the structure of the set of positive radial solutions for a class of supercritical semilinear elliptic Dirichlet boundary value problems. This structure (bifurcation diagram) is provided only at the heuristic level in many important works. In this paper, we investigate this structure, as accurately as possible, for the classof problems mentioned above taking into account the dimension of Euclidean space as well as the physical parameter involved.