Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials

Author(s)

Figueiredo, Giovany M. ^[1] ; Pimenta, Marcos T. O. ^[2]

Affiliation

^[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF - Brazil

^[2] Univ Estadual Paulista UNESP, Dept Matemat & Comp, Fac Ciencias & Tecnol, Presidente Prudente, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 459, n. 2, p. 861-878, MAR 15 2018.
• Web of Science Citations: 5

Abstract

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(R-N). 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. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 17/01756-2 - Variational methods applied to problems modeled in the space of functions of bounded variation
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Support Opportunities: Regular Research Grants
• FAPESP's process: 15/12476-5 - Existence and multiplicity of solutions to elliptic equations and systems
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil