Existence and concentration of ground state solutions for a class of nonlocal problem in [formula omitted

Abstract

In this paper, we study the following nonlocal problem in RN−a−ϵ∫RN|Δu|2dxΔu+(1+λf(x))u=|u|p−2u,where a>0, 2<p<2∗=2N∕(N−2) with N≥3, ϵ>0 is small enough, and the parameter λ>0. Under some assumptions on f(x), we prove the existence of ground state solutions for the problem when λ is large enough via variational methods. In addition, we obtain some concentration behaviors of these solutions as λ→+∞.