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arXiv · 1606.02158

A guide to the Choquard equation

Vitaly Moroz·Jean Van Schaftingen
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Abstract

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

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Vitaly Moroz, Jean Van Schaftingen. 2016-06-07. A guide to the Choquard equation. https://doi.org/10.1007/s11784-016-0373-1

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