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

Abstract

For the following singularly perturbed problem −ε2Δu+Vfalse(xfalse)u=ffalse(ufalse),u∈H1RN,N≥3,we construct a solution uε 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.