Artículos de revistas
Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials
Fecha
2018-03-15Registro en:
Journal of Mathematical Analysis and Applications, v. 459, n. 2, p. 861-878, 2018.
1096-0813
0022-247X
10.1016/j.jmaa.2017.11.014
2-s2.0-85034024361
Autor
Universidade de Brasília (UnB)
Universidade Estadual Paulista (Unesp)
Institución
Resumen
In this work it is studied a quasilinear elliptic problem in the whole space RN involving the 1-Laplacian operator, with potentials which can vanish at infinity. The Euler–Lagrange functional is defined in a space whose definition resembles BV(RN). It is proved the existence of a nonnegative nontrivial bounded variation solution and the proof relies on a version of the Mountain Pass Theorem without the Palais–Smale condition to Lipschitz continuous functionals.