Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials

The existence of positive solutions to−ε2Δu+Vu=upin RN, is proved for small ε  , where N⩾3N⩾3, V   is a nonnegative continuous potential which has a positive local minimum, and NN−2

RésuméNous prouvons l'existence de solutions positives non triviales de−ε2Δu+Vu=updans RN, pour ε   petit, où N⩾3N⩾3, V   est potentiel continu positif qui a un minimum local strictement positif et NN−2