Semi-classical states for the Choquard equation

We study the nonlocal equation - ε 2 Δ u ε + V u ε = ε - α ( I α ∗ | u ε | p ) | u ε | p - 2 u ε in R N , where N ≥ 1 , α ∈ ( 0 , N ) , I α ( x ) = A α / | x | N - α is the Riesz potential and ε > 0 is a small parameter. We show that if the external potential V ∈ C ( R N ; [ 0 , ∞ ) ) has a local...

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