Ortiz Chata, Juan C.
Pimenta, Marcos T. O.
Número total de Autores: 2
Afiliação do(s) autor(es):
 Univ Estadual Paulista Unesp, Dept Matemat, BR-14054000 Sao Jose Do Rio Preto, SP - Brazil
 Univ Estadual Paulista UNESP, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP - Brazil
Número total de Afiliações: 2
Tipo de documento:
Journal of Mathematical Analysis and Applications;
AUG 1 2021.
Citações Web of Science:
In this work we study a quasilinear elliptic problem involving the 1-Laplacian operator in R-N, whose nonlinearity satisfy conditions similar to those ones of the classical work of Berestycki and Lions. Several difficulties are faced when trying to generalize the arguments of the semilinear case, to this quasilinear problem. The main existence theorem is proved through a new version of the well known Mountain Pass Theorem to locally Lipschitz functionals, where it is considered the Cerami compactness condition rather than the Palais-Smale one. It is also proved that all bounded variation solutions which are regular enough, satisfy a Pohozaev type identity. (C) 2021 Elsevier Inc. All rights reserved. (AU)