Nodal Solutions to Quasilinear Elliptic Problems Involving the 1-Laplacian Operator via Variational and Approximation Methods

Autor(es)

Figueiredo, Giovany M. ; Pimenta, Marcos T. O.

• Tipo de documento: Artigo Científico
• Fonte: Indiana University Mathematics Journal; v. 71, n. 2, p. 24-pg., 2022-01-01.

Resumo

In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional associated with a problem involving the 1-Laplacian operator in R-N, on a subset of the Nehari set which contains just sign-changing functions. In the second part we obtain a nodal solution to a quasilinear elliptic problem involving the 1-Laplacian operator in a bounded domain, through a thorough analysis of the sequence of solutions of the p-Laplacian problem associated with it, as p -> 1(+). In both cases, several technical difficulties appear in comparison with the related results involving signed solutions. (AU)

• Processo FAPESP: 21/04158-4 - Problemas elípticos envolvendo o operador de curvatura-média no espaço das funções de variação limitada
• Beneficiário: Marcos Tadeu de Oliveira Pimenta
• Modalidade de apoio: Auxílio à Pesquisa - Regular