Energy-based localization and multiplicity of radially symmetric states for the stationary p-Laplace diffusion

It is investigated the role of the state-dependent source-term for the localization by means of the kinetic energy of radially symmetric states for the stationary p-Laplace diffusion. It is shown that the oscillatory behavior of the source-term, with respect to the state amplitude, yields multiple possible states, located in disjoint energy bands. The mathematical analysis makes use of critical point theory in conical shells and of a version of Pucci-Serrin three-critical point theorem for the intersection of a cone with a ball. A key ingredient is a Harnack type inequality in terms of the energetic norm.