Existence of a radial solution to a 1-Laplacian problem in [formula omitted

Abstract

We obtain the existence of a radial solution to the following 1-Laplacian problem −Δ1u+u|u|=Q(x)f(u),inRN,u∈BV(RN).(0.1) The work is carried out in the space of functions of bounded variation BV(RN). The proof of the main result relies on a version of mountain pass theorem without Palais–Smale condition to Lipschitz continuous functionals, and symmetric criticality principle of Palais for non-smooth functionals .