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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 500, n. 1 AUG 1 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 19/13503-7 - Problemas quasilineares elípticos com peso no espaço das funções de variação limitada
• Beneficiário: Juan Carlos Ortiz Chata
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 19/14330-9 - Problemas elípticos variacionais e não-variacionais envolvendo o operador 1-Laplaciano
• Beneficiário: Marcos Tadeu de Oliveira Pimenta
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 17/06119-0 - Problemas elípticos quasilineares no espaço das funções de variação limitada
• Beneficiário: Juan Carlos Ortiz Chata
• Modalidade de apoio: Bolsas no Brasil - Doutorado