Nodal Solutions to Quasilinear Elliptic Problems Involving the 1-Laplacian Operator via Variational and Approximation Methods
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 RN, on a sub...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/246831 |
| Acceso en línea: | http://dx.doi.org/10.1512/iumj.2022.71.8881 http://hdl.handle.net/11449/246831 |
| Access Level: | acceso abierto |
| Palabra clave: | 1-Laplacian operator Nehari method nodal solutions |
| Sumario: | 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 RN, 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. |
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