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

We obtain the existence of a radial solution to the following 1-Laplacian problem {-Delta(1)u + u vertical bar u vertical bar = Q(x)f(u), in R-N, (0.1) u is an element of BV (R-N). The work is carried out in the space of functions of bounded variation BV (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 . (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper discusses the existence of a radial solution to a 1-Laplacian problem and proves the existence of a solution in the space of functions of bounded variation BV (R-N). The proof relies on a version of mountain pass theorem and the symmetric criticality principle.