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These lecture notes are devoted to the analysis of a nonlocal
equation in the whole of Euclidean space. In studying this
equation, all the necessary material is introduced in the most
self-contained way possible, giving precise references to the
literature when necessary. The results presented are original, but
no particular prerequisite or knowledge of the previous literature
is needed to read this text. The work is accessible to a wide
audience and can also serve as introductory research material on
the topic of nonlocal nonlinear equations.
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