Existence of a ground state solution for Choquard equation with the upper critical exponent

Abstract In this paper, we investigate the following Choquard equation − Δ u + u = ( I α ∗ | u | N + α N − 2 ) | u | N + α N − 2 − 2 u + g ( u ) in R N , where N ⩾ 3 , α ∈ ( 0 , N ) , I α is the Riesz potential and g is a given function. If g satisfies the general subcritical growth conditions, we obtain the existence of a positive ground state solution.

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