Semiclassical states of p-Laplacian equations with a general nonlinearity in critical case

We consider the p-Laplacian problem $− ε p Δ p u+V ( x ) u p − 2 u=f ( u ) ,u∈ W 1 , p ( R N ) ,$ where p ∈ (1, N) and f(s) is of critical growth. In this paper, we construct a single peak solution around an isolated component of the positive local minimum points of V as ε → 0 with a general nonlinearity f. In particular, the monotonicity of f(s)/s^p−1 and the so-called Ambrosetti-Rabinowitz condition are not required.