A guide to the Choquard equation

By Vitaly Moroz, Jean Van Schaftingen. 2016

572 citations recorded by the source corpus.

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$\begin{aligned} -\Delta u + V(x)u = \left( |x|^{-(N-\alpha )} *|u |^p\right) |u |^{p - 2} u \quad \text {in} \ \mathbb {R}^N, \end{aligned}$$-Δu+V(x)u=|x|-(N-α)∗|u|p|u|p-2uinRN,and some of its variants and extensions.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/99b13ae8061d9b9e2806aa6ea05a66ded9b1cbb0

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In Applied Mathematics

1. Fashun Gao
2. Daniele Cassani
3. Jianjun Zhang
4. Minbo Yang
5. Xinfu Li
6. Marco Squassina
7. Claudianor Oliveira Alves
8. Giovany M. Figueiredo

Citations in the corpus

• Standing waves to upper critical Choquard equation with a local perturbation: Multiplicity, qualitative properties and stability (2021, background): “dx, see for example [19, 20, 26, 30] and the references therein.”
• Singularly perturbed critical Choquard equations (2016, background): “For a complete and updated discussion upon the current literature of such problems, we refer the interested reader to the guide [28].”
• Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth (2018, background): “We refer to [47] and references therein for an extensive survey on the topic.”