Normalized solutions for a fractional coupled critical Hartree system

Abstract

We consider the existence of normalized solutions for a fractional coupled Hartree system, with the upper critical exponent in the sense of the Hardy-Littelwood-Sobolev inequality. Particularly, in an $L^2$-subcritical regime or an $L^2$-supercritical regime, we establish the existence of positive normalized solutions for the two cases, respectively. Furthermore, we prove the nonexistence of positive normalized solutions, under the nonlinearities satisfying the Sobolev critical growth.

Keywords

• fractional hartree system
• normalized solutions
• hardy–littlewood–sobolev critical exponent