Normalized solutions of fractional Choquard equation with critical nonlinearity

Abstract

In this paper, we are concerned with normalized solutions of the fractional critical Choquard equation with a local perturbation and prescribed mass. For the $L^2$-subcritical case, we study the multiplicity of normalized solutions by applying the truncation technique, the concentration-compactness principle and the genus theory. For the $L^2$-supercritical case, we obtain a couple of normalized solutions by developing a fiber map and using the concentration-compactness principle.