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Ground states for nonlinear fractional Choquard equations with general nonlinearities. (English) Zbl 1344.35168

Summary: We study the existence of ground states for the nonlinear Choquard equation driven by fractional Laplacian: \[ (-\Delta)^su+u=\left(|x|^{-\mu}\ast F(u)\right)\,f(u)\text{ in }\mathbb R^n, \] where the nonlinearity satisfies the general Berestycki-Lions-type assumptions.

MSC:

35R11 Fractional partial differential equations
35J25 Boundary value problems for second-order elliptic equations
35J60 Nonlinear elliptic equations
35A15 Variational methods applied to PDEs
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