Existence of a radial solution to a 1-Laplacian problem in RN

Abstract We obtain the existence of a radial solution to the following 1-Laplacian problem − Δ 1 u + u | u | = Q ( x ) f ( u ) , in R N , u ∈ B V ( R N ) . ( 0 . 1 ) The work is carried out in the space of funcitons of bounded variation B V ( R N ) . 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 .