A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator

Author(s)

Ortiz Chata, Juan C. ^[1] ; Pimenta, Marcos T. O. ^[2]

Affiliation

^[1] Univ Estadual Paulista Unesp, Dept Matemat, BR-14054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Estadual Paulista UNESP, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 500, n. 1 AUG 1 2021.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 19/13503-7 - Weighted quasilinear elliptic problems in the space of functions of bounded variation
• Grantee: Juan Carlos Ortiz Chata
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 19/14330-9 - Variational and nonvariational elliptic problems involving the 1-Laplacian operator
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/06119-0 - Quasilinear elliptic problems in the space of functions of bounded variation
• Grantee: Juan Carlos Ortiz Chata
• Support Opportunities: Scholarships in Brazil - Doctorate