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

Author(s)

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

• Document type: Journal article
• Source: Indiana University Mathematics Journal; v. 71, n. 2, p. 24-pg., 2022-01-01.

Abstract

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)

• FAPESP's process: 21/04158-4 - Elliptic problems involving the mean-curvature operator in the space of functions of bounded variation
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Support Opportunities: Regular Research Grants