On existence and concentration of positive solutions for a fractional Kirchhoff equation with critical exponential growth

In this paper we consider the following fractional Kirchhoff type problem { ( epsilon a+epsilon b/2 pi integral R-2|u(x)-u(y)|(2)|x-y|2dxdy) (-Delta)12u+V(x)u=f(u)inR. u is an element of H1/2(R),u>0 where epsilon is a positive parameter and a,b > 0 are constants; V is a positive continuous potential and f is a nonlinear term with critical exponential growth in the Trudinger-Moser sense. We obtain the existence and concentration of positive solutions by variational methods.