A Berestycki-Lions type result for a class of problems involving the 1-Laplacian operator

In this work we prove a Berestycki-Lions type result for the following class of problems: -Delta(1)u + u/vertical bar u vertical bar = f(u) in R-N, u is an element of BV (R-N), where Delta(1) is the 1-Laplacian operator and f is a continuous function satisfying some technical conditions. Here we apply variational methods by using p-Laplacian problems and taking the limit when p -> 1(+).

Automated summary

In this work, we prove a Berestycki-Lions type result for a specific class of problems, where we apply variational methods and p-Laplacian problems, and take the limit as p approaches 1(+).