Artículos de revistas
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator
Fecha
2021-08-01Registro en:
Journal of Mathematical Analysis and Applications, v. 500, n. 1, 2021.
1096-0813
0022-247X
10.1016/j.jmaa.2021.125074
2-s2.0-85101176994
Autor
Universidade Estadual Paulista (Unesp)
Institución
Resumen
In this work we study a quasilinear elliptic problem involving the 1-Laplacian operator in RN, 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.