Normalized solutions of fractional mass supercritical NLS systems with linear couplings

Abstract

In this paper, we consider normalized solutions for fractional NLS systems with Sobolev critical nonlinearities and linear couplings. Under mass supercritical condition, there are two cases discussed. First, we use the minimax method to get the existence of positive normalized solution when the exponent is Sobolev subcritical. Second, if it is Sobolev critical, we prove the nonexistence of positive normalized solution. Scaling transformation and concentration-compactness principle are used in this paper.