A critical fractional Choquard–Kirchhoff problem with magnetic field

In this paper, we are interested in a fractional Choquard–Kirchhoff-type problem involving an external magnetic potential and a critical nonlinearity Formula: see text Formula: see text where Formula: see text with Formula: see text, Formula: see text is the Kirchhoff function, Formula: see text is the magnetic potential, Formula: see text is the fractional magnetic operator, Formula: see text is a continuous function, Formula: see text, Formula: see text is a parameter, Formula: see text and Formula: see text is the critical exponent of fractional Sobolev space. We first establish a fractional version of the concentration-compactness principle with magnetic field. Then, together with the mountain pass theorem, we obtain the existence of nontrivial radial solutions for the above problem in non-degenerate and degenerate cases.