LEAST ENERGY SOLUTIONS FOR NONLINEAR FRACTIONAL CHOQUARD–KIRCHHOFF EQUATIONS IN RN

In this paper, we investigate the following fractional Choquard–Kirchhoff type equation: (Formula presented) where N ≥ 2, a, b > 0 are constants, (−∆)s is the fractional Laplacian operator of order s ∈ (0, 1), Iα denotes the Riesz potential of order α ∈ ((N − 4s)+, N), F ∈ C1(R) is a general nonlinearity of Berestycki–Lions type. Applying suitable variational methods, we prove the existence of a least energy solution. Moreover, assuming that F is even and monotone in (0, ∞), we show that the constructed solution has constant sign, is radially symmetric and decreasing.