Existence and concentration of ground state solutions for an equation with steep potential well and exponential critical growth

Abstract

In this paper we study the existence and concentration of ground state solution for the following class of elliptic equations{−div(a(|∇u|p)|∇u|p−2∇u)+(1+μV(x))b(|u|p)|u|p−2u=f(u)in RN,u∈W1,p(RN)∩W1,N(RN), where 1<p≤N, N≥2, μ>0 is a parameter, the functions a,b∈C1(R) and the nonlinearity f has an exponential critical growth. To show the existence and concentration results we obtain interesting estimates which do not depend on μ.