Normalized ground states for the fractional Schr?dinger-Poisson system with critical nonlinearities

In this paper we study the existence and properties of ground states for the fractional Schr & ouml;dinger-Poisson system with combined power nonlinearities {(-)su-phi|u|2 & lowast;s-3u=lambda u+mu|u|q-2u+|u|2 & lowast;s-2u,x is an element of R3,(-)s phi=|u|2 & lowast;s-1,x is an element of R3, having prescribed mass integral(R3)|u|2dx=a(2 ) and doubly critical growth, where is an element of(0,1),mu>0 is a parameter, 2 0+is also studied. Our results complement and improve theexisting ones in several directions, and this study seems to be the first contribution regarding existence of normalized ground states for the fractional Sobolev critical Schr & ouml;dinger-Poissonsystem with a critical nonlocal term.