Existence and Profile of Ground-State Solutions to a 1-Laplacian Problem in RN
In this work we prove the existence of ground state solutions for the following class of problems {-Δ1u+(1+λV(x))u|u|=f(u),x∈RN,u∈BV(RN),where λ> 0 , Δ 1 denotes the 1-Laplacian operator which is formally defined by Δ1u=div(∇u/|∇u|), V: RN→ R is a potential satisfying some conditions and f: R→ R...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/199658 |
| Acceso en línea: | http://dx.doi.org/10.1007/s00574-019-00179-4 http://hdl.handle.net/11449/199658 |
| Access Level: | acceso abierto |
| Palabra clave: | 1-Laplacian operator Bounded variation functions Concentration results |
| Sumario: | In this work we prove the existence of ground state solutions for the following class of problems {-Δ1u+(1+λV(x))u|u|=f(u),x∈RN,u∈BV(RN),where λ> 0 , Δ 1 denotes the 1-Laplacian operator which is formally defined by Δ1u=div(∇u/|∇u|), V: RN→ R is a potential satisfying some conditions and f: R→ R is a subcritical nonlinearity. We prove that for λ> 0 large enough there exist ground-state solutions and, as λ→ + ∞, such solutions converges to a ground-state solution of the limit problem in Ω=int(V-1({0})). |
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