Ground states for nonlinear fractional Choquard equations with general nonlinearities

Abstract

We study the existence of ground states for the nonlinear Choquard equation driven by fractional Laplacian:where the nonlinearity satisfies the general Berestycki-Lions-type assumptions.

Existence of solutions for fractional $p$-Kirchhoff type equations with a generalized Choquard nonlinearity

“…In particular, they claimed the nonexistence of solutions as q ∈ ( 2N−µ N , 2N−µ N−2s ). If V(x) = 1 and f satisfies Berestycki-Lions type assumptions, the existence of ground state solutions for a fractional Choquard equation has been established in [31]. Very recently, Ambrosio studied the concentration phenomena of solutions for a fractional Choquard equation with mangetic field in [4].…”

On doubly nonlocal $p$-fractional coupled elliptic system

“…Wu in [50] proved the existence of standing waves by studying the related constrained minimization problems via the concentration-compactness principle for the following nonlinear fractional Schrödinger equations with Hartree type nonlinearity iψ t + (−∆) α ψ − (| · | −γ * |ψ| 2 )ψ = 0, where 0 < α < 1, 0 < γ < 2α and ψ(x, t) is a complex-valued function on R d × R, d ≥ 1. Some recent works on Schödinger equations with fractional Laplacian equation includes [14,19,39,43] with no attempt to provide a complete list. Existence of solutions for the equation of the type −∆u + w(x)u = (I α * |u| p )|u| p−2 u in R n , where w(x) is appropriate function, I α is Reisz potential and p > 1 is chosen appropriately, have been studied in [2,13,22,35,49].…”

On the multiplicity and concentration of positive solutions for a p-fractional Choquard equation in RN

“…Shen et al [49] investigated the existence of ground state solutions for a fractional Choquard equation involving a general nonlinearity. In [7] the author used penalization technique and Ljusternik-Schnirelmann theory to study the multiplicity and concentration of positive solutions to…”