Abstract
ABSTRACT The first aim of this paper is to classify the positive solutions of the fractional Choquard equation where is the upper critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality. Moreover, based on the uniqueness and non-degeneracy of the solution of the above equation, we then study the perturbed Choquard equation By using the finite-dimensional reduction, we obtain the existence of at least one positive solution if is suitable small.
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