On the dynamics of a strongly singular parabolic equation

In this paper we study the semiflow defined by a semilinear parabolic equation, in which both the diffusion and the reaction term present strong order of singularity at the origin. We justify the existence of a global branch of nontrivial equilibrium solutions for subcritical nonlinearities. The approach, based on the critical Caffarelli–Kohn–Nirenberg inequality, follows the arguments of [21] and [22].