Standing waves for nonlinear Schrodinger equations involving critical growth

We consider the following singularly perturbed nonlinear elliptic problem: −ε2Δu + V (x)u = f(u), u∈ H1(RN), where N ≥ 3 and f is the nonlinearity of critical growth. In this paper, we construct a solution uε of the above problem, which concentrates at an isolated component of the positive local minimum points of V as ε → 0 under certain conditions on f. Our result completes th…