Non-radial ground state solutions for fractional Schrödinger–Poisson systems in ℝ2

Note: Please see pdf for full abstract with equations. In this paper, we study the fractional Schrödinger–Poisson system with general nonlinearity as follows: (−∆) s u + u + l(x)φu = ƒ(u) in R 2 , (−∆) t φ = l(x)u 2 in R 2 , where 1/2 < t ≤ s 0 is a parameter, by establishing new estimates for the fractional Laplacian, we find two positive solutions, depending on the range of µ . As a result, a positive ground state solution with negative energy exists for the non-autonomous system without any symmetry on l(x) . When l(x) is radially symmetric, we show that the symmetry breaking phenomenon can occur, and that a non-radial ground state solution with negative energy exists. Furthermore, under additional assumptions on l(x) , three positive solutions are found. The intrinsic differences between the planar SP system and the planar fSP system are analyzed. 2020 Mathematics Subject Classification. Primary: 35B38; Secondary: 35J60