Energy–based localization and multiplicity of radially symmetric states for the stationary p–Laplace diffusion. Issue 7 (2nd July 2020) - Precup, Radu; Pucci, Patrizia; Varga, Csaba
ABSTRACT: 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.