Existence and concentration result for fractional Choquard equations in $$\pmb {{\mathbb {R}}^{N}}$$

Ground state solutions for a class of fractional Kirchhoff-Choquard equations

“…For the case V (x) = w, F (u) = |u| p , the regularity, existence, nonexistence, symmetry and decay properties of solutions for (1.2) has been obtained by d'Aenia, Siciliano and Squassina [1]. Subsequently, these results were extended to more general potential V and nonlinearity f , see [2,3].…”

“…Meanwhile, the study of Choquard-type equations has received extensive attention due to its wide application in physical models. For instance, Che, Su and Chen [2] considered the existence of ground state solution for the fractional Choquard equations with competing potentials. Su and Shi [13] studied the existence of solutions for quasilinear Choquard equation with critical exponent.…”

“…It is worth noting that we have to restrict s ∈ (0, 2 3 ) when N = 2 in the process of proving the existence of ground state solutions of the corresponding limit problem. For more details, see Lemma 3.5.…”

Ground states for nonlinear fractional Schrödinger–Poisson systems with general convolution nonlinearities

“…For instance, Teng and Agarwal [19] established the existence of nonnegative ground state solution and also discussed the nonexistence of ground states to (1.4) with subcritical Choquard nonlinearity. Che et al [20] obtained the existence of ground state solution for fractional Choquard equations with competing potentials.…”

Ground state solutions for fractional Choquard-Schrödinger-Poisson system with critical growth

“…where 3+µ 3 < p < 3+µ 3−2s , 1 < q < p. For instance, Teng and Agarwal [20] established the existence of non-negative ground state solution and also discussed the nonexistence of ground states to (1.4) with subcritical Choquard nonlinearity. Che, Su, and Chen [21] obtained the existence of ground state solutions for fractional Choquard equations with competing potentials. The authors in [22,23] recently studied quasilinear versions of the Choquard equation with the p-Laplace operator, and obtained the existence and nonexistence of positive solutions for the quasilinear elliptic inequalities and systems with nonlocal terms.…”