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

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We consider the p-Laplacian problem -εpΔpu + V(x)|u|p-2u = f(u), u ∈ W1,p(ℝN), 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)/sp-1 and the so-called Ambrosetti-Rabinowitz condition are not required.