Existence of a nontrivial solution for a (p,q)-Laplacian equation with p-critical exponent in RN
In this paper we prove the existence of a nontrivial solution in D1,p(RN)∩D1,q(RN) for the following (p,q)-Laplacian problem: {−Δpu−Δqu=λg(x)|u|r−1u+|u|p⋆−2u,u(x)≥0,x∈RN, where 1<q≤p<r+1<p⋆:=NpN−p, p<N, λ>0 is a parameter, Δmu:=div(|∇u|m−2∇u) is the m-Laplacian operator and g∈Lp⋆p⋆−r−...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Brasil |
| Recursos: | Universidade Federal de Lavras (UFLA) |
| Repositorio: | Repositório Institucional da UFLA |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.ufla.br:1/45523 |
| Acesso em linha: | https://repositorio.ufla.br/handle/1/45523 |
| Access Level: | acceso abierto |
| Palavra-chave: | Critical exponent Nonnegative solution (p,q)$(p,q)$-Laplacian equation Equação de Laplace Expoente crítico Solução não negativa |
| Resumo: | In this paper we prove the existence of a nontrivial solution in D1,p(RN)∩D1,q(RN) for the following (p,q)-Laplacian problem: {−Δpu−Δqu=λg(x)|u|r−1u+|u|p⋆−2u,u(x)≥0,x∈RN, where 1<q≤p<r+1<p⋆:=NpN−p, p<N, λ>0 is a parameter, Δmu:=div(|∇u|m−2∇u) is the m-Laplacian operator and g∈Lp⋆p⋆−r−1(RN) is positive in an open set. MSC: 35J92, 47J30. |
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