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A guide to the Choquard equation. (English) Zbl 1360.35252

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

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35R09 Integro-partial differential equations
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
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