Concentration behavior of solutions for fractional Schrödinger equations involving critical exponent

In this paper, we study the following fractional Schrodinger equation involving critical exponent e2s(−Δ)su+V(x)u=|u|2s*−2u+λf(u), x∈RN, where 0 2s, 2s*=2NN−2s, λ > 0, and f is a continuous superlinear but subcritical function. Under some suitable conditions, we obtain the concentration behavior of solutions for the above equation. This improves the results in the work of Shang and Zhang [Nonlinearity 27, 187–207 (2014)].