Concentrating solutions for a fractional Kirchhoff equation with critical growth

In this paper we consider the following class of fractional Kirchhoff equations with critical growth: (equations presented) where ϵ > 0 is a small parameter, a, b > 0 are constants, s ϵ (3/4, 1), 2∗s = 6/3-2s is the fractional critical exponent, (-δ)s is the fractional Laplacian operator, V is a positive continuous potential and f is a superlinear continuous function with subcritical growth. Using penalization techniques and variational methods, we prove the existence of a family of positive solutions uϵ which concentrates around a local minimum of V as ϵ → 0.