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arxiv: 1606.02158 · v1 · pith:TBNHCON2new · submitted 2016-06-07 · 🧮 math.AP

A guide to the Choquard equation

Vitaly Moroz , Jean Van Schaftingen This is my paper
classification 🧮 math.AP
keywords choquardalphabiglbigrdealingdeltaequationequations
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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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