Existence and Profile of Ground-State Solutions to a 1-Laplacian Problem in RN

• Autor(a) principal: Alves, Claudianor O.
• Data de Publicação: 2020
• Outros Autores: Figueiredo, Giovany M., Pimenta, Marcos T. O. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s00574-019-00179-4; http://hdl.handle.net/11449/199658
• topic: 1-Laplacian operator; Bounded variation functions; Concentration results

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})).