Multiplicity of solutions for a class of quasilinear problems involving the 1-Laplacian operator with critical growth
The aim of this paper is to establish two results about multiplicity of solutions to problems involving the 1-Laplacian operator, with nonlinearities with critical growth. To be more specific, we study the following problem [Formula presented] where Ω is a smooth bounded domain in RN, N≥2 and ξ∈{0,1...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Brasil |
| Recursos: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/229915 |
| Acesso em linha: | http://dx.doi.org/10.1016/j.jde.2021.11.012 http://hdl.handle.net/11449/229915 |
| Access Level: | acceso abierto |
| Palavra-chave: | 1-Laplacian Functions of bounded variation Operator Variational methods |
| Resumo: | The aim of this paper is to establish two results about multiplicity of solutions to problems involving the 1-Laplacian operator, with nonlinearities with critical growth. To be more specific, we study the following problem [Formula presented] where Ω is a smooth bounded domain in RN, N≥2 and ξ∈{0,1}. Moreover, λ>0, q∈(1,1⁎) and [Formula presented]. The first main result establishes the existence of many rotationally non-equivalent and nonradial solutions by assuming that ξ=1, Ω={x∈RN:r<|x|<r+1}, N≥2, N≠3 and r>0. In the second one, Ω is a smooth bounded domain, ξ=0, and the multiplicity of solutions is proved through an abstract result which involves genus theory for functionals which are sum of a C1 functional with a convex lower semicontinuous functional. |
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