Multi‐peak standing waves for nonlinear Schrödinger equations involving critical growth

For the following singularly perturbed problem − ε 2 Δ u + V ( x ) u = f ( u ) ,u ∈ H 1R N , N ≥ 3 , we construct a solution u ε which concentrates at several given isolated positive local minimum components of V as ε → 0 . Here, the nonlinearity f is of critical growth. Moreover, the monotonicity of f ( s ) / s and the so‐called Ambrosetti–Rabinowitz condition are not required.