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

Author(s)

Alves, Claudianor O. ^[1] ; Figueiredo, Giovany M. ^[2] ; Pimenta, Marcos T. O. ^[3]

Affiliation

^[1] Univ Fed Campina Grande, Unidade Acad Matemat & Estat, BR-58429900 Campina Grande - Brazil

^[2] Univ Brasilia UNB, Dept Matemat, BR-70910900 Brasilia, DF - Brazil

^[3] Univ Estadual Paulista, Fac Ciencias & Tecnol, UNESP, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP - Brazil

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 51, n. 3 NOV 2019.
• Web of Science Citations: 0

Abstract

In this work we prove the existence of ground state solutions for the following class of problems -Delta 1u+(1+lambda V(x))u|u|=f(u),x is an element of RN,u is an element of BV(RN), denotes the 1-Laplacian operator which is formally defined by Delta 1u=div( backward difference u/ backward difference u|) is a potential satisfying some conditions and f:R -> R is a subcritical nonlinearity. We prove that for lambda>0 large enough there exist ground-state solutions and, as lambda ->+infinity, such solutions converges to a ground-state solution of the limit problem in omega=int(V-1([0])). (AU)

• FAPESP's process: 19/14330-9 - Variational and nonvariational elliptic problems involving the 1-Laplacian operator
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Support Opportunities: Regular Research Grants