Existence and concentration behavior of solutions to 1-Laplace equations on [formula omitted

Abstract

In this paper, the following 1-Laplace equation−εDiv(Du/|Du|)+a(x)u/|u|=h(u)(x∈RN) in BV space is considered, where ε>0 is a small parameter, N≥2; and a:RN→R, h:R→R are suitable functions. The existence of bounded variation solutions are obtained by employing the nonsmooth critical point theorem. Furthermore, the concentration behavior of the solutions are studied and a single spike shape of the solutions is proved when the parameter ε is small enough.