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

摘要

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})).