A guide to the Choquard equation

Published 7 Jun 2016 in math.AP | (1606.02158v1)

Abstract: We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$ -\Delta u + V(x)u = \bigl(|x|^{{-(N-\alpha)}} * |u|^{p\bigr)|u|^{p} - 2} u \qquad \text{in $\mathbb{R}^N$}, $$ and some of its variants and extensions.

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